%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : GRP167-4 : TPTP v8.2.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : do_cvc5 %s %d

% Computer : n024.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 16:53:29 EDT 2024

% Result   : Unsatisfiable 18.53s 18.76s
% Output   : Proof 18.60s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13  % Problem    : GRP167-4 : TPTP v8.2.0. Bugfixed v1.2.1.
% 0.06/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n024.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Sun May 26 18:50:39 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.21/0.50  %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.50  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.53/10.79  --- Run --no-e-matching --full-saturate-quant at 5...
% 15.60/15.82  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 18.53/18.76  % SZS status Unsatisfiable for /export/starexec/sandbox2/tmp/tmp.jkiYFG9902/cvc5---1.0.5_29032.smt2
% 18.53/18.76  % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.jkiYFG9902/cvc5---1.0.5_29032.smt2
% 18.60/18.82  (assume a0 (forall ((X $$unsorted)) (= (tptp.multiply tptp.identity X) X)))
% 18.60/18.82  (assume a1 (forall ((X $$unsorted)) (= (tptp.multiply (tptp.inverse X) X) tptp.identity)))
% 18.60/18.82  (assume a2 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 18.60/18.82  (assume a3 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))))
% 18.60/18.82  (assume a4 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))))
% 18.60/18.82  (assume a5 (forall ((X $$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))))
% 18.60/18.82  (assume a6 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))))
% 18.60/18.82  (assume a7 (forall ((X $$unsorted)) (= (tptp.least_upper_bound X X) X)))
% 18.60/18.82  (assume a8 (forall ((X $$unsorted)) (= (tptp.greatest_lower_bound X X) X)))
% 18.60/18.82  (assume a9 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)) X)))
% 18.60/18.82  (assume a10 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)) X)))
% 18.60/18.82  (assume a11 (forall ((X $$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)))))
% 18.60/18.82  (assume a12 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))))
% 18.60/18.82  (assume a13 (forall ((Y $$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)))))
% 18.60/18.82  (assume a14 (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))))
% 18.60/18.82  (assume a15 (= (tptp.inverse tptp.identity) tptp.identity))
% 18.60/18.82  (assume a16 (forall ((X $$unsorted)) (= (tptp.inverse (tptp.inverse X)) X)))
% 18.60/18.82  (assume a17 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))))
% 18.60/18.82  (assume a18 (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))))
% 18.60/18.82  (step t1 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (forall ((X $$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)
% 18.60/18.82  (anchor :step t2)
% 18.60/18.82  (assume t2.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))))
% 18.60/18.82  (step t2.t1 (cl (or (not (forall ((X $$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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) :rule forall_inst :args ((:= X (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (:= Y (tptp.greatest_lower_bound tptp.a tptp.identity)) (:= Z tptp.a)))
% 18.60/18.82  (step t2.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) :rule or :premises (t2.t1))
% 18.60/18.82  (step t2.t3 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) :rule resolution :premises (t2.t2 t2.a0))
% 18.60/18.82  (step t2 (cl (not (forall ((X $$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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) :rule subproof :discharge (t2.a0))
% 18.60/18.82  (step t3 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) :rule resolution :premises (t1 t2))
% 18.60/18.82  (step t4 (cl (=> (forall ((X $$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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) :rule implies_neg2)
% 18.60/18.82  (step t5 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (=> (forall ((X $$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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) :rule resolution :premises (t3 t4))
% 18.60/18.82  (step t6 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) :rule contraction :premises (t5))
% 18.60/18.82  (step t7 (cl (not (forall ((X $$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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) :rule implies :premises (t6))
% 18.60/18.82  (step t8 (cl (not (= (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (or (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))))) (not (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))))) (or (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))))) :rule equiv_pos2)
% 18.60/18.82  (step t9 (cl (= (= (= (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) true) (= (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule equiv_simplify)
% 18.60/18.82  (step t10 (cl (not (= (= (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) true)) (= (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule equiv1 :premises (t9))
% 18.60/18.82  (step t11 (cl (= (= (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))))))) :rule all_simplify)
% 18.60/18.82  (step t12 (cl (= (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule refl)
% 18.60/18.82  (step t13 (cl (= (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule all_simplify)
% 18.60/18.82  (step t14 (cl (= (= (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule cong :premises (t12 t13))
% 18.60/18.82  (step t15 (cl (= (= (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) true)) :rule all_simplify)
% 18.60/18.82  (step t16 (cl (= (= (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))))) true)) :rule trans :premises (t14 t15))
% 18.60/18.82  (step t17 (cl (= (= (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) true)) :rule trans :premises (t11 t16))
% 18.60/18.82  (step t18 (cl (= (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule resolution :premises (t10 t17))
% 18.60/18.82  (step t19 (cl (= (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) :rule refl)
% 18.60/18.82  (step t20 (cl (= (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))))) :rule refl)
% 18.60/18.82  (step t21 (cl (= (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))))) :rule refl)
% 18.60/18.82  (step t22 (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)
% 18.60/18.82  (step t23 (cl (= (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))))) :rule refl)
% 18.60/18.82  (step t24 (cl (= (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))))) :rule refl)
% 18.60/18.82  (step t25 (cl (= (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))))) :rule refl)
% 18.60/18.82  (step t26 (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)
% 18.60/18.82  (step t27 (cl (= (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule refl)
% 18.60/18.82  (step t28 (cl (= (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule refl)
% 18.60/18.82  (step t29 (cl (= (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))))) :rule refl)
% 18.60/18.82  (step t30 (cl (= (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))))) :rule refl)
% 18.60/18.82  (step t31 (cl (= (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))))) :rule refl)
% 18.60/18.82  (step t32 (cl (= (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))))) :rule refl)
% 18.60/18.82  (step t33 (cl (= (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule refl)
% 18.60/18.82  (step t34 (cl (= (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))))) :rule refl)
% 18.60/18.82  (step t35 (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)
% 18.60/18.82  (step t36 (cl (= (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))))) :rule refl)
% 18.60/18.82  (step t37 (cl (= (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))))) :rule refl)
% 18.60/18.82  (step t38 (cl (= (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))))) :rule refl)
% 18.60/18.82  (step t39 (cl (= (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))))) :rule refl)
% 18.60/18.82  (step t40 (cl (= (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule refl)
% 18.60/18.82  (step t41 (cl (= (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))))) :rule refl)
% 18.60/18.82  (step t42 (cl (= (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule refl)
% 18.60/18.82  (step t43 (cl (= (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))))) :rule refl)
% 18.60/18.82  (step t44 (cl (= (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))))) :rule refl)
% 18.60/18.82  (step t45 (cl (= (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))))) :rule refl)
% 18.60/18.82  (step t46 (cl (= (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))))) :rule refl)
% 18.60/18.82  (step t47 (cl (= (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))))) :rule refl)
% 18.60/18.82  (step t48 (cl (= (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))))) :rule refl)
% 18.60/18.82  (step t49 (cl (= (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))))) :rule refl)
% 18.60/18.82  (step t50 (cl (= (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))))) :rule refl)
% 18.60/18.82  (step t51 (cl (= (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (or (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))))) :rule cong :premises (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))
% 18.60/18.82  (step t52 (cl (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule and_neg)
% 18.60/18.82  (step t53 (cl (=> (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule implies_neg1)
% 18.60/18.82  (anchor :step t54)
% 18.60/18.82  (assume t54.a0 (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))))
% 18.60/18.82  (assume t54.a1 (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))
% 18.60/18.82  (assume t54.a2 (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))
% 18.60/18.82  (assume t54.a3 (= tptp.a (tptp.multiply tptp.identity tptp.a)))
% 18.60/18.82  (assume t54.a4 (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))
% 18.60/18.82  (assume t54.a5 (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)))
% 18.60/18.82  (assume t54.a6 (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)))
% 18.60/18.82  (assume t54.a7 (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))))
% 18.60/18.82  (assume t54.a8 (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))
% 18.60/18.82  (assume t54.a9 (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))
% 18.60/18.82  (assume t54.a10 (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))
% 18.60/18.82  (assume t54.a11 (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)))
% 18.60/18.82  (assume t54.a12 (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)))
% 18.60/18.82  (assume t54.a13 (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))))
% 18.60/18.82  (assume t54.a14 (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)))
% 18.60/18.82  (assume t54.a15 (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))
% 18.60/18.82  (assume t54.a16 (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))
% 18.60/18.82  (assume t54.a17 (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))
% 18.60/18.82  (assume t54.a18 (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))))
% 18.60/18.82  (assume t54.a19 (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)))
% 18.60/18.82  (assume t54.a20 (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))))
% 18.60/18.82  (assume t54.a21 (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))
% 18.60/18.82  (assume t54.a22 (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))
% 18.60/18.82  (assume t54.a23 (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))))
% 18.60/18.82  (assume t54.a24 (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))
% 18.60/18.82  (assume t54.a25 (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))
% 18.60/18.82  (assume t54.a26 (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))))
% 18.60/18.82  (assume t54.a27 (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))))
% 18.60/18.82  (assume t54.a28 (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))))
% 18.60/18.82  (assume t54.a29 (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))))
% 18.60/18.82  (assume t54.a30 (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))))
% 18.60/18.82  (assume t54.a31 (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))
% 18.60/18.82  (step t54.t1 (cl (=> (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) :rule implies_neg1)
% 18.60/18.82  (anchor :step t54.t2)
% 18.60/18.82  (assume t54.t2.a0 (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))
% 18.60/18.82  (assume t54.t2.a1 (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))
% 18.60/18.82  (assume t54.t2.a2 (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))
% 18.60/18.82  (assume t54.t2.a3 (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))
% 18.60/18.82  (assume t54.t2.a4 (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))
% 18.60/18.82  (assume t54.t2.a5 (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))))
% 18.60/18.82  (assume t54.t2.a6 (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))
% 18.60/18.82  (assume t54.t2.a7 (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)))
% 18.60/18.82  (assume t54.t2.a8 (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)))
% 18.60/18.82  (assume t54.t2.a9 (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))))
% 18.60/18.82  (assume t54.t2.a10 (= tptp.a (tptp.multiply tptp.identity tptp.a)))
% 18.60/18.82  (assume t54.t2.a11 (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))))
% 18.60/18.82  (assume t54.t2.a12 (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))))
% 18.60/18.82  (assume t54.t2.a13 (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)))
% 18.60/18.82  (assume t54.t2.a14 (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))
% 18.60/18.82  (assume t54.t2.a15 (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))
% 18.60/18.82  (assume t54.t2.a16 (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))))
% 18.60/18.82  (assume t54.t2.a17 (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))))
% 18.60/18.82  (assume t54.t2.a18 (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)))
% 18.60/18.82  (assume t54.t2.a19 (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))))
% 18.60/18.82  (assume t54.t2.a20 (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))
% 18.60/18.82  (assume t54.t2.a21 (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)))
% 18.60/18.82  (assume t54.t2.a22 (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))))
% 18.60/18.82  (assume t54.t2.a23 (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))
% 18.60/18.82  (assume t54.t2.a24 (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))
% 18.60/18.82  (assume t54.t2.a25 (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))
% 18.60/18.82  (assume t54.t2.a26 (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)))
% 18.60/18.82  (assume t54.t2.a27 (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))))
% 18.60/18.82  (assume t54.t2.a28 (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))
% 18.60/18.82  (assume t54.t2.a29 (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))))
% 18.60/18.82  (assume t54.t2.a30 (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))))
% 18.60/18.82  (assume t54.t2.a31 (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))
% 18.60/18.82  (step t54.t2.t1 (cl (= (= (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) false) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))))) :rule equiv_simplify)
% 18.60/18.82  (step t54.t2.t2 (cl (not (= (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) false)) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) :rule equiv1 :premises (t54.t2.t1))
% 18.60/18.82  (step t54.t2.t3 (cl (= (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule refl)
% 18.60/18.82  (step t54.t2.t4 (cl (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule symm :premises (t54.t2.a8))
% 18.60/18.82  (step t54.t2.t5 (cl (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) :rule refl)
% 18.60/18.82  (step t54.t2.t6 (cl (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule cong :premises (t54.t2.a21 t54.t2.t5))
% 18.60/18.82  (step t54.t2.t7 (cl (= (tptp.least_upper_bound tptp.a tptp.a) tptp.a)) :rule symm :premises (t54.t2.a21))
% 18.60/18.82  (step t54.t2.t8 (cl (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) :rule symm :premises (t54.t2.a6))
% 18.60/18.82  (step t54.t2.t9 (cl (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) :rule symm :premises (t54.t2.t8))
% 18.60/18.82  (step t54.t2.t10 (cl (= tptp.identity tptp.identity)) :rule refl)
% 18.60/18.82  (step t54.t2.t11 (cl (= (tptp.greatest_lower_bound tptp.a tptp.a) tptp.a)) :rule symm :premises (t54.t2.a26))
% 18.60/18.82  (step t54.t2.t12 (cl (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) :rule symm :premises (t54.t2.t11))
% 18.60/18.82  (step t54.t2.t13 (cl (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)))) :rule cong :premises (t54.t2.t10 t54.t2.t12))
% 18.60/18.82  (step t54.t2.t14 (cl (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a) (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)))) :rule symm :premises (t54.t2.a7))
% 18.60/18.82  (step t54.t2.t15 (cl (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) :rule symm :premises (t54.t2.t14))
% 18.60/18.82  (step t54.t2.t16 (cl (= tptp.a tptp.a)) :rule refl)
% 18.60/18.82  (step t54.t2.t17 (cl (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) :rule cong :premises (t54.t2.t8 t54.t2.t16))
% 18.60/18.82  (step t54.t2.t18 (cl (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule symm :premises (t54.t2.a13))
% 18.60/18.82  (step t54.t2.t19 (cl (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule trans :premises (t54.t2.t9 t54.t2.t13 t54.t2.t15 t54.t2.t17 t54.t2.t18))
% 18.60/18.82  (step t54.t2.t20 (cl (= (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule cong :premises (t54.t2.t7 t54.t2.t19))
% 18.60/18.82  (step t54.t2.t21 (cl (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.a)) :rule symm :premises (t54.t2.a12))
% 18.60/18.82  (step t54.t2.t22 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.identity)) :rule symm :premises (t54.t2.a23))
% 18.60/18.82  (step t54.t2.t23 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity tptp.a))) :rule cong :premises (t54.t2.t22 t54.t2.t16))
% 18.60/18.82  (step t54.t2.t24 (cl (= (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a))) :rule symm :premises (t54.t2.t23))
% 18.60/18.82  (step t54.t2.t25 (cl (= (tptp.inverse (tptp.inverse tptp.a)) tptp.a)) :rule symm :premises (t54.t2.a24))
% 18.60/18.82  (step t54.t2.t26 (cl (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule symm :premises (t54.t2.t25))
% 18.60/18.82  (step t54.t2.t27 (cl (= (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)) :rule symm :premises (t54.t2.a25))
% 18.60/18.82  (step t54.t2.t28 (cl (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule symm :premises (t54.t2.t27))
% 18.60/18.82  (step t54.t2.t29 (cl (= (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule cong :premises (t54.t2.t26 t54.t2.t28))
% 18.60/18.82  (step t54.t2.t30 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a tptp.identity))) :rule symm :premises (t54.t2.t29))
% 18.60/18.82  (step t54.t2.t31 (cl (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a) (tptp.multiply tptp.a tptp.identity))) :rule trans :premises (t54.t2.t4 t54.t2.t6 t54.t2.t20 t54.t2.t21 t54.t2.a10 t54.t2.t24 t54.t2.a2 t54.t2.t30))
% 18.60/18.82  (step t54.t2.t32 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) :rule cong :premises (t54.t2.t3 t54.t2.t31))
% 18.60/18.82  (step t54.t2.t33 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)) (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) :rule symm :premises (t54.t2.a22))
% 18.60/18.82  (step t54.t2.t34 (cl (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) :rule symm :premises (t54.t2.a14))
% 18.60/18.82  (step t54.t2.t35 (cl (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule symm :premises (t54.t2.t34))
% 18.60/18.82  (step t54.t2.t36 (cl (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) :rule cong :premises (t54.t2.t10 t54.t2.t9))
% 18.60/18.82  (step t54.t2.t37 (cl (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) tptp.identity)) :rule symm :premises (t54.t2.a4))
% 18.60/18.82  (step t54.t2.t38 (cl (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) tptp.identity)) :rule trans :premises (t54.t2.t35 t54.t2.t36 t54.t2.t37))
% 18.60/18.82  (step t54.t2.t39 (cl (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.multiply tptp.a tptp.identity))) :rule cong :premises (t54.t2.t16 t54.t2.t38))
% 18.60/18.82  (step t54.t2.t40 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a))) :rule symm :premises (t54.t2.a2))
% 18.60/18.82  (step t54.t2.t41 (cl (= (tptp.multiply tptp.identity tptp.a) tptp.a)) :rule symm :premises (t54.t2.a10))
% 18.60/18.82  (step t54.t2.t42 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) tptp.a)) :rule trans :premises (t54.t2.t32 t54.t2.t33 t54.t2.t39 t54.t2.t29 t54.t2.t40 t54.t2.t23 t54.t2.t41))
% 18.60/18.82  (step t54.t2.t43 (cl (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) :rule symm :premises (t54.t2.a0))
% 18.60/18.82  (step t54.t2.t44 (cl (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule symm :premises (t54.t2.t43))
% 18.60/18.82  (step t54.t2.t45 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule cong :premises (t54.t2.t3 t54.t2.t44))
% 18.60/18.82  (step t54.t2.t46 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule symm :premises (t54.t2.a20))
% 18.60/18.82  (step t54.t2.t47 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule trans :premises (t54.t2.t45 t54.t2.t46))
% 18.60/18.82  (step t54.t2.t48 (cl (= (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) :rule cong :premises (t54.t2.t47 t54.t2.t16))
% 18.60/18.82  (step t54.t2.t49 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule refl)
% 18.60/18.82  (step t54.t2.t50 (cl (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) :rule symm :premises (t54.t2.a1))
% 18.60/18.82  (step t54.t2.t51 (cl (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) :rule symm :premises (t54.t2.t50))
% 18.60/18.82  (step t54.t2.t52 (cl (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))) tptp.a)) :rule symm :premises (t54.t2.a31))
% 18.60/18.82  (step t54.t2.t53 (cl (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) :rule symm :premises (t54.t2.t52))
% 18.60/18.82  (step t54.t2.t54 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) :rule symm :premises (t54.t2.a18))
% 18.60/18.82  (step t54.t2.t55 (cl (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) :rule symm :premises (t54.t2.t54))
% 18.60/18.82  (step t54.t2.t56 (cl (= (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.a))) :rule refl)
% 18.60/18.82  (step t54.t2.t57 (cl (= (tptp.multiply tptp.a tptp.identity) tptp.a)) :rule trans :premises (t54.t2.t29 t54.t2.t40 t54.t2.t23 t54.t2.t41))
% 18.60/18.82  (step t54.t2.t58 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) :rule cong :premises (t54.t2.t56 t54.t2.t57))
% 18.60/18.82  (step t54.t2.t59 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) :rule symm :premises (t54.t2.t58))
% 18.60/18.82  (step t54.t2.t60 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) :rule symm :premises (t54.t2.a30))
% 18.60/18.82  (step t54.t2.t61 (cl (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) :rule trans :premises (t54.t2.t55 t54.t2.t59 t54.t2.t60))
% 18.60/18.82  (step t54.t2.t62 (cl (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) :rule cong :premises (t54.t2.t12 t54.t2.t61))
% 18.60/18.82  (step t54.t2.t63 (cl (= tptp.a (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) :rule trans :premises (t54.t2.t53 t54.t2.t62))
% 18.60/18.82  (step t54.t2.t64 (cl (= (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) :rule symm :premises (t54.t2.a3))
% 18.60/18.82  (step t54.t2.t65 (cl (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) :rule symm :premises (t54.t2.t64))
% 18.60/18.82  (step t54.t2.t66 (cl (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) :rule cong :premises (t54.t2.t63 t54.t2.t65))
% 18.60/18.82  (step t54.t2.t67 (cl (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule symm :premises (t54.t2.a19))
% 18.60/18.82  (step t54.t2.t68 (cl (= (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound tptp.a tptp.a))) :rule refl)
% 18.60/18.82  (step t54.t2.t69 (cl (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) :rule symm :premises (t54.t2.t60))
% 18.60/18.82  (step t54.t2.t70 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) :rule cong :premises (t54.t2.t56 t54.t2.a10))
% 18.60/18.82  (step t54.t2.t71 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) :rule symm :premises (t54.t2.a5))
% 18.60/18.82  (step t54.t2.t72 (cl (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) :rule trans :premises (t54.t2.t69 t54.t2.t58 t54.t2.t70 t54.t2.t71))
% 18.60/18.82  (step t54.t2.t73 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) :rule symm :premises (t54.t2.a29))
% 18.60/18.82  (step t54.t2.t74 (cl (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) :rule symm :premises (t54.t2.t73))
% 18.60/18.82  (step t54.t2.t75 (cl (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) :rule refl)
% 18.60/18.82  (step t54.t2.t76 (cl (= (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule cong :premises (t54.t2.t74 t54.t2.t75))
% 18.60/18.82  (step t54.t2.t77 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule symm :premises (t54.t2.a27))
% 18.60/18.82  (step t54.t2.t78 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule symm :premises (t54.t2.t77))
% 18.60/18.82  (step t54.t2.t79 (cl (= (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity))) :rule symm :premises (t54.t2.a9))
% 18.60/18.82  (step t54.t2.t80 (cl (= (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) :rule symm :premises (t54.t2.a15))
% 18.60/18.82  (step t54.t2.t81 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.identity))) :rule cong :premises (t54.t2.t79 t54.t2.t80))
% 18.60/18.82  (step t54.t2.t82 (cl (= (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) :rule trans :premises (t54.t2.t76 t54.t2.t78 t54.t2.t81))
% 18.60/18.82  (step t54.t2.t83 (cl (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) :rule cong :premises (t54.t2.t72 t54.t2.t82))
% 18.60/18.82  (step t54.t2.t84 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule symm :premises (t54.t2.a17))
% 18.60/18.82  (step t54.t2.t85 (cl (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule trans :premises (t54.t2.t83 t54.t2.t84))
% 18.60/18.82  (step t54.t2.t86 (cl (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule cong :premises (t54.t2.t68 t54.t2.t85))
% 18.60/18.82  (step t54.t2.t87 (cl (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule cong :premises (t54.t2.t11 t54.t2.t49))
% 18.60/18.82  (step t54.t2.t88 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule symm :premises (t54.t2.a28))
% 18.60/18.82  (step t54.t2.t89 (cl (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) :rule symm :premises (t54.t2.t88))
% 18.60/18.82  (step t54.t2.t90 (cl (= tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) :rule trans :premises (t54.t2.t51 t54.t2.t66 t54.t2.t67 t54.t2.t86 t54.t2.t87 t54.t2.t89))
% 18.60/18.82  (step t54.t2.t91 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) :rule cong :premises (t54.t2.t49 t54.t2.t90))
% 18.60/18.82  (step t54.t2.t92 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule symm :premises (t54.t2.a16))
% 18.60/18.82  (step t54.t2.t93 (cl (= (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule trans :premises (t54.t2.t48 t54.t2.t91 t54.t2.t92))
% 18.60/18.82  (step t54.t2.t94 (cl (= (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule cong :premises (t54.t2.t42 t54.t2.t93))
% 18.60/18.82  (step t54.t2.t95 (cl (= (= (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) false) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule equiv_simplify)
% 18.60/18.82  (step t54.t2.t96 (cl (= (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) false) (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule equiv2 :premises (t54.t2.t95))
% 18.60/18.82  (step t54.t2.t97 (cl (not (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule not_not)
% 18.60/18.82  (step t54.t2.t98 (cl (= (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) false) (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule resolution :premises (t54.t2.t96 t54.t2.t97))
% 18.60/18.82  (step t54.t2.t99 (cl (= (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) false)) :rule resolution :premises (t54.t2.t98 t54.t2.a11))
% 18.60/18.82  (step t54.t2.t100 (cl (= (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) false)) :rule trans :premises (t54.t2.t94 t54.t2.t99))
% 18.60/18.82  (step t54.t2.t101 (cl (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) :rule resolution :premises (t54.t2.t2 t54.t2.t100))
% 18.60/18.82  (step t54.t2 (cl (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) :rule subproof :discharge (t54.t2.a0 t54.t2.a1 t54.t2.a2 t54.t2.a3 t54.t2.a4 t54.t2.a5 t54.t2.a6 t54.t2.a7 t54.t2.a8 t54.t2.a9 t54.t2.a10 t54.t2.a11 t54.t2.a12 t54.t2.a13 t54.t2.a14 t54.t2.a15 t54.t2.a16 t54.t2.a17 t54.t2.a18 t54.t2.a19 t54.t2.a20 t54.t2.a21 t54.t2.a22 t54.t2.a23 t54.t2.a24 t54.t2.a25 t54.t2.a26 t54.t2.a27 t54.t2.a28 t54.t2.a29 t54.t2.a30 t54.t2.a31))
% 18.60/18.82  (step t54.t3 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule and_pos)
% 18.60/18.82  (step t54.t4 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) :rule and_pos)
% 18.60/18.82  (step t54.t5 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule and_pos)
% 18.60/18.82  (step t54.t6 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) :rule and_pos)
% 18.60/18.82  (step t54.t7 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) :rule and_pos)
% 18.60/18.82  (step t54.t8 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) :rule and_pos)
% 18.60/18.82  (step t54.t9 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) :rule and_pos)
% 18.60/18.82  (step t54.t10 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) :rule and_pos)
% 18.60/18.82  (step t54.t11 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) :rule and_pos)
% 18.60/18.82  (step t54.t12 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) :rule and_pos)
% 18.60/18.82  (step t54.t13 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) :rule and_pos)
% 18.60/18.82  (step t54.t14 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule and_pos)
% 18.60/18.82  (step t54.t15 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule and_pos)
% 18.60/18.82  (step t54.t16 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) :rule and_pos)
% 18.60/18.82  (step t54.t17 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule and_pos)
% 18.60/18.82  (step t54.t18 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule and_pos)
% 18.60/18.82  (step t54.t19 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) :rule and_pos)
% 18.60/18.82  (step t54.t20 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) :rule and_pos)
% 18.60/18.82  (step t54.t21 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) :rule and_pos)
% 18.60/18.82  (step t54.t22 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) :rule and_pos)
% 18.60/18.82  (step t54.t23 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule and_pos)
% 18.60/18.82  (step t54.t24 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) :rule and_pos)
% 18.60/18.82  (step t54.t25 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) :rule and_pos)
% 18.60/18.82  (step t54.t26 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule and_pos)
% 18.60/18.82  (step t54.t27 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule and_pos)
% 18.60/18.82  (step t54.t28 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule and_pos)
% 18.60/18.82  (step t54.t29 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) :rule and_pos)
% 18.60/18.82  (step t54.t30 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule and_pos)
% 18.60/18.82  (step t54.t31 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) :rule and_pos)
% 18.60/18.82  (step t54.t32 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) :rule and_pos)
% 18.60/18.82  (step t54.t33 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) :rule and_pos)
% 18.60/18.82  (step t54.t34 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) :rule and_pos)
% 18.60/18.82  (step t54.t35 (cl (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))))) :rule resolution :premises (t54.t2 t54.t3 t54.t4 t54.t5 t54.t6 t54.t7 t54.t8 t54.t9 t54.t10 t54.t11 t54.t12 t54.t13 t54.t14 t54.t15 t54.t16 t54.t17 t54.t18 t54.t19 t54.t20 t54.t21 t54.t22 t54.t23 t54.t24 t54.t25 t54.t26 t54.t27 t54.t28 t54.t29 t54.t30 t54.t31 t54.t32 t54.t33 t54.t34))
% 18.60/18.82  (step t54.t36 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) :rule reordering :premises (t54.t35))
% 18.60/18.83  (step t54.t37 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) :rule contraction :premises (t54.t36))
% 18.60/18.83  (step t54.t38 (cl (=> (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) :rule resolution :premises (t54.t1 t54.t37))
% 18.60/18.83  (step t54.t39 (cl (=> (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))))) :rule implies_neg2)
% 18.60/18.83  (step t54.t40 (cl (=> (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (=> (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))))) :rule resolution :premises (t54.t38 t54.t39))
% 18.60/18.83  (step t54.t41 (cl (=> (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))))) :rule contraction :premises (t54.t40))
% 18.60/18.83  (step t54.t42 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) :rule implies :premises (t54.t41))
% 18.60/18.83  (step t54.t43 (cl (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) :rule and_neg)
% 18.60/18.83  (step t54.t44 (cl (and (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) :rule resolution :premises (t54.t43 t54.a15 t54.a8 t54.a22 t54.a9 t54.a16 t54.a20 t54.a1 t54.a14 t54.a12 t54.a7 t54.a3 t54.a0 t54.a13 t54.a11 t54.a24 t54.a10 t54.a26 t54.a28 t54.a19 t54.a29 t54.a31 t54.a5 t54.a30 t54.a17 t54.a2 t54.a4 t54.a6 t54.a27 t54.a25 t54.a18 t54.a23 t54.a21))
% 18.60/18.83  (step t54.t45 (cl (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) :rule resolution :premises (t54.t42 t54.t44))
% 18.60/18.83  (step t54 (cl (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) :rule subproof :discharge (t54.a0 t54.a1 t54.a2 t54.a3 t54.a4 t54.a5 t54.a6 t54.a7 t54.a8 t54.a9 t54.a10 t54.a11 t54.a12 t54.a13 t54.a14 t54.a15 t54.a16 t54.a17 t54.a18 t54.a19 t54.a20 t54.a21 t54.a22 t54.a23 t54.a24 t54.a25 t54.a26 t54.a27 t54.a28 t54.a29 t54.a30 t54.a31))
% 18.60/18.83  (step t55 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule and_pos)
% 18.60/18.83  (step t56 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) :rule and_pos)
% 18.60/18.83  (step t57 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule and_pos)
% 18.60/18.83  (step t58 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) :rule and_pos)
% 18.60/18.83  (step t59 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule and_pos)
% 18.60/18.83  (step t60 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) :rule and_pos)
% 18.60/18.83  (step t61 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) :rule and_pos)
% 18.60/18.83  (step t62 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) :rule and_pos)
% 18.60/18.83  (step t63 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) :rule and_pos)
% 18.60/18.83  (step t64 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) :rule and_pos)
% 18.60/18.83  (step t65 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule and_pos)
% 18.60/18.83  (step t66 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) :rule and_pos)
% 18.60/18.83  (step t67 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) :rule and_pos)
% 18.60/18.83  (step t68 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule and_pos)
% 18.60/18.83  (step t69 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) :rule and_pos)
% 18.60/18.83  (step t70 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule and_pos)
% 18.60/18.83  (step t71 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) :rule and_pos)
% 18.60/18.83  (step t72 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule and_pos)
% 18.60/18.83  (step t73 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) :rule and_pos)
% 18.60/18.83  (step t74 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) :rule and_pos)
% 18.60/18.83  (step t75 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) :rule and_pos)
% 18.60/18.83  (step t76 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) :rule and_pos)
% 18.60/18.83  (step t77 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule and_pos)
% 18.60/18.83  (step t78 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) :rule and_pos)
% 18.60/18.83  (step t79 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule and_pos)
% 18.60/18.83  (step t80 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) :rule and_pos)
% 18.60/18.83  (step t81 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) :rule and_pos)
% 18.60/18.83  (step t82 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule and_pos)
% 18.60/18.83  (step t83 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) :rule and_pos)
% 18.60/18.83  (step t84 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) :rule and_pos)
% 18.60/18.83  (step t85 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) :rule and_pos)
% 18.60/18.83  (step t86 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule and_pos)
% 18.60/18.83  (step t87 (cl (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))))) :rule resolution :premises (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))
% 18.60/18.83  (step t88 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) :rule reordering :premises (t87))
% 18.60/18.83  (step t89 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) :rule contraction :premises (t88))
% 18.60/18.83  (step t90 (cl (=> (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) :rule resolution :premises (t53 t89))
% 18.60/18.83  (step t91 (cl (=> (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))))) :rule implies_neg2)
% 18.60/18.83  (step t92 (cl (=> (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (=> (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))))) :rule resolution :premises (t90 t91))
% 18.60/18.83  (step t93 (cl (=> (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))))) :rule contraction :premises (t92))
% 18.60/18.83  (step t94 (cl (not (and (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) :rule implies :premises (t93))
% 18.60/18.83  (step t95 (cl (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) :rule resolution :premises (t52 t94))
% 18.60/18.83  (step t96 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))))) :rule or_neg)
% 18.60/18.83  (step t97 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) :rule or_neg)
% 18.60/18.83  (step t98 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))))) :rule or_neg)
% 18.60/18.83  (step t99 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (not (= tptp.a (tptp.multiply tptp.identity tptp.a))))) :rule or_neg)
% 18.60/18.83  (step t100 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule or_neg)
% 18.60/18.83  (step t101 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))))) :rule or_neg)
% 18.60/18.83  (step t102 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))))) :rule or_neg)
% 18.60/18.83  (step t103 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))))) :rule or_neg)
% 18.60/18.83  (step t104 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule or_neg)
% 18.60/18.83  (step t105 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule or_neg)
% 18.60/18.83  (step t106 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule or_neg)
% 18.60/18.83  (step t107 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))))) :rule or_neg)
% 18.60/18.83  (step t108 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))))) :rule or_neg)
% 18.60/18.83  (step t109 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))))) :rule or_neg)
% 18.60/18.83  (step t110 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))))) :rule or_neg)
% 18.60/18.83  (step t111 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule or_neg)
% 18.60/18.83  (step t112 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))))) :rule or_neg)
% 18.60/18.83  (step t113 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) :rule or_neg)
% 18.60/18.83  (step t114 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))))) :rule or_neg)
% 18.60/18.83  (step t115 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))))) :rule or_neg)
% 18.60/18.83  (step t116 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))))) :rule or_neg)
% 18.60/18.83  (step t117 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))))) :rule or_neg)
% 18.60/18.83  (step t118 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule or_neg)
% 18.60/18.83  (step t119 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))))) :rule or_neg)
% 18.60/18.83  (step t120 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule or_neg)
% 18.60/18.83  (step t121 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))))) :rule or_neg)
% 18.60/18.83  (step t122 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))))) :rule or_neg)
% 18.60/18.83  (step t123 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))))) :rule or_neg)
% 18.60/18.83  (step t124 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))))) :rule or_neg)
% 18.60/18.83  (step t125 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))))) :rule or_neg)
% 18.60/18.83  (step t126 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))))) :rule or_neg)
% 18.60/18.83  (step t127 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))))) :rule or_neg)
% 18.60/18.83  (step t128 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))))) :rule or_neg)
% 18.60/18.83  (step t129 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) 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))
% 18.60/18.83  (step t130 (cl (or (not (not (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))))) :rule contraction :premises (t129))
% 18.60/18.83  (step t131 (cl (or (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))))) :rule resolution :premises (t8 t51 t130))
% 18.60/18.83  (step t132 (cl (= tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (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)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) :rule or :premises (t131))
% 18.60/18.83  (step t133 (cl (not (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_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.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_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.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) :rule equiv_pos2)
% 18.60/18.83  (step t134 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))))) :rule refl)
% 18.60/18.83  (step t135 (cl (= (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) :rule all_simplify)
% 18.60/18.83  (step t136 (cl (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_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.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) :rule cong :premises (t134 t135))
% 18.60/18.83  (step t137 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_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)
% 18.60/18.83  (anchor :step t138)
% 18.60/18.83  (assume t138.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))))
% 18.60/18.83  (step t138.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.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule forall_inst :args ((:= X tptp.identity) (:= Y tptp.a)))
% 18.60/18.83  (step t138.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.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) :rule or :premises (t138.t1))
% 18.60/18.83  (step t138.t3 (cl (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) :rule resolution :premises (t138.t2 t138.a0))
% 18.60/18.83  (step t138 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) :rule subproof :discharge (t138.a0))
% 18.60/18.83  (step t139 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) :rule resolution :premises (t137 t138))
% 18.60/18.83  (step t140 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule implies_neg2)
% 18.60/18.83  (step t141 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_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.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule resolution :premises (t139 t140))
% 18.60/18.83  (step t142 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule contraction :premises (t141))
% 18.60/18.83  (step t143 (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.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) :rule resolution :premises (t133 t136 t142))
% 18.60/18.83  (step t144 (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.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) :rule implies :premises (t143))
% 18.60/18.83  (step t145 (cl (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) :rule resolution :premises (t144 a3))
% 18.60/18.83  (step t146 (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)
% 18.60/18.83  (anchor :step t147)
% 18.60/18.83  (assume t147.a0 (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))))
% 18.60/18.83  (step t147.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))) :rule forall_inst :args ((:= X tptp.a)))
% 18.60/18.83  (step t147.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule or :premises (t147.t1))
% 18.60/18.83  (step t147.t3 (cl (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule resolution :premises (t147.t2 t147.a0))
% 18.60/18.83  (step t147 (cl (not (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule subproof :discharge (t147.a0))
% 18.60/18.83  (step t148 (cl (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule resolution :premises (t146 t147))
% 18.60/18.83  (step t149 (cl (=> (forall ((X $$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)
% 18.60/18.83  (step t150 (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 (t148 t149))
% 18.60/18.83  (step t151 (cl (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))) :rule contraction :premises (t150))
% 18.60/18.83  (step t152 (cl (not (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule implies :premises (t151))
% 18.60/18.83  (step t153 (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)
% 18.60/18.83  (anchor :step t154 :args ((X $$unsorted) (:= X X)))
% 18.60/18.83  (step t154.t1 (cl (= X X)) :rule refl)
% 18.60/18.83  (step t154.t2 (cl (= (= (tptp.inverse (tptp.inverse X)) X) (= X (tptp.inverse (tptp.inverse X))))) :rule all_simplify)
% 18.60/18.83  (step t154 (cl (= (forall ((X $$unsorted)) (= (tptp.inverse (tptp.inverse X)) X)) (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))))) :rule bind)
% 18.60/18.83  (step t155 (cl (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) :rule resolution :premises (t153 t154 a16))
% 18.60/18.83  (step t156 (cl (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule resolution :premises (t152 t155))
% 18.60/18.83  (step t157 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) :rule implies_neg1)
% 18.60/18.83  (anchor :step t158)
% 18.60/18.83  (assume t158.a0 (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))))
% 18.60/18.83  (step t158.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)))) :rule forall_inst :args ((:= X tptp.a)))
% 18.60/18.83  (step t158.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) :rule or :premises (t158.t1))
% 18.60/18.83  (step t158.t3 (cl (= tptp.a (tptp.multiply tptp.identity tptp.a))) :rule resolution :premises (t158.t2 t158.a0))
% 18.60/18.83  (step t158 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) :rule subproof :discharge (t158.a0))
% 18.60/18.83  (step t159 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) :rule resolution :premises (t157 t158))
% 18.60/18.83  (step t160 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a)))) :rule implies_neg2)
% 18.60/18.83  (step t161 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.a (tptp.multiply tptp.identity tptp.a)))) :rule resolution :premises (t159 t160))
% 18.60/18.83  (step t162 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.a (tptp.multiply tptp.identity tptp.a)))) :rule contraction :premises (t161))
% 18.60/18.83  (step t163 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) :rule implies :premises (t162))
% 18.60/18.83  (step t164 (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)
% 18.60/18.83  (anchor :step t165 :args ((X $$unsorted) (:= X X)))
% 18.60/18.83  (step t165.t1 (cl (= X X)) :rule refl)
% 18.60/18.83  (step t165.t2 (cl (= (= (tptp.multiply tptp.identity X) X) (= X (tptp.multiply tptp.identity X)))) :rule all_simplify)
% 18.60/18.83  (step t165 (cl (= (forall ((X $$unsorted)) (= (tptp.multiply tptp.identity X) X)) (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))))) :rule bind)
% 18.60/18.83  (step t166 (cl (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) :rule resolution :premises (t164 t165 a0))
% 18.60/18.83  (step t167 (cl (= tptp.a (tptp.multiply tptp.identity tptp.a))) :rule resolution :premises (t163 t166))
% 18.60/18.83  (step t168 (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)
% 18.60/18.83  (anchor :step t169)
% 18.60/18.83  (assume t169.a0 (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))))
% 18.60/18.83  (step t169.t1 (cl (or (not (forall ((X $$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)))
% 18.60/18.83  (step t169.t2 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule or :premises (t169.t1))
% 18.60/18.83  (step t169.t3 (cl (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule resolution :premises (t169.t2 t169.a0))
% 18.60/18.83  (step t169 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule subproof :discharge (t169.a0))
% 18.60/18.83  (step t170 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule resolution :premises (t168 t169))
% 18.60/18.83  (step t171 (cl (=> (forall ((X $$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)
% 18.60/18.83  (step t172 (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 (t170 t171))
% 18.60/18.83  (step t173 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule contraction :premises (t172))
% 18.60/18.83  (step t174 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule implies :premises (t173))
% 18.60/18.83  (step t175 (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)
% 18.60/18.83  (anchor :step t176 :args ((X $$unsorted) (:= X X)))
% 18.60/18.83  (step t176.t1 (cl (= X X)) :rule refl)
% 18.60/18.83  (step t176.t2 (cl (= (= (tptp.multiply (tptp.inverse X) X) tptp.identity) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) :rule all_simplify)
% 18.60/18.83  (step t176 (cl (= (forall ((X $$unsorted)) (= (tptp.multiply (tptp.inverse X) X) tptp.identity)) (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))))) :rule bind)
% 18.60/18.83  (step t177 (cl (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) :rule resolution :premises (t175 t176 a1))
% 18.60/18.83  (step t178 (cl (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule resolution :premises (t174 t177))
% 18.60/18.83  (step t179 (cl (=> (forall ((X $$unsorted)) (= X (tptp.least_upper_bound X X))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (forall ((X $$unsorted)) (= X (tptp.least_upper_bound X X)))) :rule implies_neg1)
% 18.60/18.83  (anchor :step t180)
% 18.60/18.83  (assume t180.a0 (forall ((X $$unsorted)) (= X (tptp.least_upper_bound X X))))
% 18.60/18.83  (step t180.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.least_upper_bound X X)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)))) :rule forall_inst :args ((:= X tptp.a)))
% 18.60/18.83  (step t180.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.least_upper_bound X X)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) :rule or :premises (t180.t1))
% 18.60/18.83  (step t180.t3 (cl (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) :rule resolution :premises (t180.t2 t180.a0))
% 18.60/18.83  (step t180 (cl (not (forall ((X $$unsorted)) (= X (tptp.least_upper_bound X X)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) :rule subproof :discharge (t180.a0))
% 18.60/18.83  (step t181 (cl (=> (forall ((X $$unsorted)) (= X (tptp.least_upper_bound X X))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) :rule resolution :premises (t179 t180))
% 18.60/18.83  (step t182 (cl (=> (forall ((X $$unsorted)) (= X (tptp.least_upper_bound X X))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (not (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)))) :rule implies_neg2)
% 18.60/18.83  (step t183 (cl (=> (forall ((X $$unsorted)) (= X (tptp.least_upper_bound X X))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) (=> (forall ((X $$unsorted)) (= X (tptp.least_upper_bound X X))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)))) :rule resolution :premises (t181 t182))
% 18.60/18.83  (step t184 (cl (=> (forall ((X $$unsorted)) (= X (tptp.least_upper_bound X X))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a)))) :rule contraction :premises (t183))
% 18.60/18.83  (step t185 (cl (not (forall ((X $$unsorted)) (= X (tptp.least_upper_bound X X)))) (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) :rule implies :premises (t184))
% 18.60/18.83  (step t186 (cl (not (= (forall ((X $$unsorted)) (= (tptp.least_upper_bound X X) X)) (forall ((X $$unsorted)) (= X (tptp.least_upper_bound X X))))) (not (forall ((X $$unsorted)) (= (tptp.least_upper_bound X X) X))) (forall ((X $$unsorted)) (= X (tptp.least_upper_bound X X)))) :rule equiv_pos2)
% 18.60/18.83  (anchor :step t187 :args ((X $$unsorted) (:= X X)))
% 18.60/18.83  (step t187.t1 (cl (= X X)) :rule refl)
% 18.60/18.83  (step t187.t2 (cl (= (= (tptp.least_upper_bound X X) X) (= X (tptp.least_upper_bound X X)))) :rule all_simplify)
% 18.60/18.83  (step t187 (cl (= (forall ((X $$unsorted)) (= (tptp.least_upper_bound X X) X)) (forall ((X $$unsorted)) (= X (tptp.least_upper_bound X X))))) :rule bind)
% 18.60/18.83  (step t188 (cl (forall ((X $$unsorted)) (= X (tptp.least_upper_bound X X)))) :rule resolution :premises (t186 t187 a7))
% 18.60/18.83  (step t189 (cl (= tptp.a (tptp.least_upper_bound tptp.a tptp.a))) :rule resolution :premises (t185 t188))
% 18.60/18.83  (step t190 (cl (=> (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X))) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X)))) :rule implies_neg1)
% 18.60/18.83  (anchor :step t191)
% 18.60/18.83  (assume t191.a0 (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X))))
% 18.60/18.83  (step t191.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X)))) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)))) :rule forall_inst :args ((:= X tptp.a)))
% 18.60/18.83  (step t191.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X)))) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) :rule or :premises (t191.t1))
% 18.60/18.83  (step t191.t3 (cl (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) :rule resolution :premises (t191.t2 t191.a0))
% 18.60/18.83  (step t191 (cl (not (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X)))) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) :rule subproof :discharge (t191.a0))
% 18.60/18.83  (step t192 (cl (=> (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X))) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) :rule resolution :premises (t190 t191))
% 18.60/18.83  (step t193 (cl (=> (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X))) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)))) :rule implies_neg2)
% 18.60/18.83  (step t194 (cl (=> (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X))) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) (=> (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X))) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)))) :rule resolution :premises (t192 t193))
% 18.60/18.83  (step t195 (cl (=> (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X))) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a)))) :rule contraction :premises (t194))
% 18.60/18.83  (step t196 (cl (not (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X)))) (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) :rule implies :premises (t195))
% 18.60/18.83  (step t197 (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)
% 18.60/18.83  (anchor :step t198 :args ((X $$unsorted) (:= X X)))
% 18.60/18.83  (step t198.t1 (cl (= X X)) :rule refl)
% 18.60/18.83  (step t198.t2 (cl (= (= (tptp.greatest_lower_bound X X) X) (= X (tptp.greatest_lower_bound X X)))) :rule all_simplify)
% 18.60/18.83  (step t198 (cl (= (forall ((X $$unsorted)) (= (tptp.greatest_lower_bound X X) X)) (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X))))) :rule bind)
% 18.60/18.83  (step t199 (cl (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X)))) :rule resolution :premises (t197 t198 a8))
% 18.60/18.83  (step t200 (cl (= tptp.a (tptp.greatest_lower_bound tptp.a tptp.a))) :rule resolution :premises (t196 t199))
% 18.60/18.83  (step t201 (cl (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) :rule implies_neg1)
% 18.60/18.83  (anchor :step t202)
% 18.60/18.83  (assume t202.a0 (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))))
% 18.60/18.83  (step t202.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule forall_inst :args ((:= X (tptp.least_upper_bound tptp.a tptp.identity))))
% 18.60/18.83  (step t202.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) :rule or :premises (t202.t1))
% 18.60/18.83  (step t202.t3 (cl (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) :rule resolution :premises (t202.t2 t202.a0))
% 18.60/18.83  (step t202 (cl (not (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) :rule subproof :discharge (t202.a0))
% 18.60/18.83  (step t203 (cl (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) :rule resolution :premises (t201 t202))
% 18.60/18.83  (step t204 (cl (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule implies_neg2)
% 18.60/18.83  (step t205 (cl (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule resolution :premises (t203 t204))
% 18.60/18.83  (step t206 (cl (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule contraction :premises (t205))
% 18.60/18.83  (step t207 (cl (not (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) :rule implies :premises (t206))
% 18.60/18.83  (step t208 (cl (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) :rule resolution :premises (t207 t155))
% 18.60/18.83  (step t209 (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)
% 18.60/18.83  (anchor :step t210)
% 18.60/18.83  (assume t210.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))))
% 18.60/18.83  (step t210.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)))
% 18.60/18.83  (step t210.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 (t210.t1))
% 18.60/18.83  (step t210.t3 (cl (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) :rule resolution :premises (t210.t2 t210.a0))
% 18.60/18.83  (step t210 (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 (t210.a0))
% 18.60/18.83  (step t211 (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 (t209 t210))
% 18.60/18.83  (step t212 (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)
% 18.60/18.83  (step t213 (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 (t211 t212))
% 18.60/18.83  (step t214 (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 (t213))
% 18.60/18.83  (step t215 (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 (t214))
% 18.60/18.83  (step t216 (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)
% 18.60/18.83  (anchor :step t217 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y)))
% 18.60/18.83  (step t217.t1 (cl (= X X)) :rule refl)
% 18.60/18.83  (step t217.t2 (cl (= Y Y)) :rule refl)
% 18.60/18.83  (step t217.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)
% 18.60/18.83  (step t217 (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)
% 18.60/18.83  (step t218 (cl (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) :rule resolution :premises (t216 t217 a10))
% 18.60/18.83  (step t219 (cl (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) :rule resolution :premises (t215 t218))
% 18.60/18.83  (step t220 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) :rule implies_neg1)
% 18.60/18.83  (anchor :step t221)
% 18.60/18.83  (assume t221.a0 (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))))
% 18.60/18.83  (step t221.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) :rule forall_inst :args ((:= X (tptp.least_upper_bound tptp.a tptp.identity))))
% 18.60/18.83  (step t221.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) :rule or :premises (t221.t1))
% 18.60/18.83  (step t221.t3 (cl (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) :rule resolution :premises (t221.t2 t221.a0))
% 18.60/18.83  (step t221 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) :rule subproof :discharge (t221.a0))
% 18.60/18.83  (step t222 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) :rule resolution :premises (t220 t221))
% 18.60/18.83  (step t223 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) :rule implies_neg2)
% 18.60/18.83  (step t224 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) :rule resolution :premises (t222 t223))
% 18.60/18.83  (step t225 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) :rule contraction :premises (t224))
% 18.60/18.83  (step t226 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) :rule implies :premises (t225))
% 18.60/18.83  (step t227 (cl (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) :rule resolution :premises (t226 t166))
% 18.60/18.83  (step t228 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) :rule implies_neg1)
% 18.60/18.83  (anchor :step t229)
% 18.60/18.83  (assume t229.a0 (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))))
% 18.60/18.83  (step t229.t1 (cl (or (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule forall_inst :args ((:= X (tptp.least_upper_bound tptp.a tptp.identity))))
% 18.60/18.83  (step t229.t2 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule or :premises (t229.t1))
% 18.60/18.83  (step t229.t3 (cl (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule resolution :premises (t229.t2 t229.a0))
% 18.60/18.83  (step t229 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule subproof :discharge (t229.a0))
% 18.60/18.83  (step t230 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule resolution :premises (t228 t229))
% 18.60/18.83  (step t231 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule implies_neg2)
% 18.60/18.83  (step t232 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule resolution :premises (t230 t231))
% 18.60/18.83  (step t233 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule contraction :premises (t232))
% 18.60/18.83  (step t234 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule implies :premises (t233))
% 18.60/18.83  (step t235 (cl (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule resolution :premises (t234 t177))
% 18.60/18.83  (step t236 (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_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)
% 18.60/18.83  (anchor :step t237)
% 18.60/18.83  (assume t237.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))))
% 18.60/18.83  (step t237.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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)))) :rule forall_inst :args ((:= X tptp.a) (:= Y (tptp.greatest_lower_bound tptp.a tptp.identity))))
% 18.60/18.83  (step t237.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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) :rule or :premises (t237.t1))
% 18.60/18.83  (step t237.t3 (cl (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) :rule resolution :premises (t237.t2 t237.a0))
% 18.60/18.83  (step t237 (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) :rule subproof :discharge (t237.a0))
% 18.60/18.83  (step t238 (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) :rule resolution :premises (t236 t237))
% 18.60/18.83  (step t239 (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)))) :rule implies_neg2)
% 18.60/18.83  (step t240 (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)))) :rule resolution :premises (t238 t239))
% 18.60/18.83  (step t241 (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)))) :rule contraction :premises (t240))
% 18.60/18.83  (step t242 (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) :rule implies :premises (t241))
% 18.60/18.83  (step t243 (cl (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) :rule resolution :premises (t242 a3))
% 18.60/18.83  (step t244 (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) :rule implies_neg1)
% 18.60/18.83  (anchor :step t245)
% 18.60/18.83  (assume t245.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))))
% 18.60/18.83  (step t245.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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)))) :rule forall_inst :args ((:= X tptp.a) (:= Y (tptp.greatest_lower_bound tptp.a tptp.identity))))
% 18.60/18.83  (step t245.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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) :rule or :premises (t245.t1))
% 18.60/18.83  (step t245.t3 (cl (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) :rule resolution :premises (t245.t2 t245.a0))
% 18.60/18.83  (step t245 (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) :rule subproof :discharge (t245.a0))
% 18.60/18.83  (step t246 (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) :rule resolution :premises (t244 t245))
% 18.60/18.83  (step t247 (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)))) :rule implies_neg2)
% 18.60/18.83  (step t248 (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a 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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)))) :rule resolution :premises (t246 t247))
% 18.60/18.83  (step t249 (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)))) :rule contraction :premises (t248))
% 18.60/18.83  (step t250 (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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) :rule implies :premises (t249))
% 18.60/18.83  (step t251 (cl (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a))) :rule resolution :premises (t250 a4))
% 18.60/18.83  (step t252 (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.greatest_lower_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)
% 18.60/18.83  (anchor :step t253)
% 18.60/18.83  (assume t253.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))))
% 18.60/18.83  (step t253.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.greatest_lower_bound tptp.a tptp.identity)))))) :rule forall_inst :args ((:= X tptp.a) (:= Y (tptp.greatest_lower_bound tptp.a tptp.identity))))
% 18.60/18.83  (step t253.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.greatest_lower_bound tptp.a tptp.identity))))) :rule or :premises (t253.t1))
% 18.60/18.83  (step t253.t3 (cl (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule resolution :premises (t253.t2 t253.a0))
% 18.60/18.83  (step t253 (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.greatest_lower_bound tptp.a tptp.identity))))) :rule subproof :discharge (t253.a0))
% 18.60/18.83  (step t254 (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.greatest_lower_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule resolution :premises (t252 t253))
% 18.60/18.83  (step t255 (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.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule implies_neg2)
% 18.60/18.83  (step t256 (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.greatest_lower_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.greatest_lower_bound tptp.a tptp.identity)))))) :rule resolution :premises (t254 t255))
% 18.60/18.83  (step t257 (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.greatest_lower_bound tptp.a tptp.identity)))))) :rule contraction :premises (t256))
% 18.60/18.83  (step t258 (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.greatest_lower_bound tptp.a tptp.identity))))) :rule implies :premises (t257))
% 18.60/18.83  (step t259 (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)
% 18.60/18.83  (anchor :step t260 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y)))
% 18.60/18.83  (step t260.t1 (cl (= X X)) :rule refl)
% 18.60/18.83  (step t260.t2 (cl (= Y Y)) :rule refl)
% 18.60/18.83  (step t260.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)
% 18.60/18.83  (step t260 (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)
% 18.60/18.83  (step t261 (cl (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) :rule resolution :premises (t259 t260 a9))
% 18.60/18.83  (step t262 (cl (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule resolution :premises (t258 t261))
% 18.60/18.83  (step t263 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (forall ((X $$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)
% 18.60/18.83  (anchor :step t264)
% 18.60/18.83  (assume t264.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z))))
% 18.60/18.83  (step t264.t1 (cl (or (not (forall ((X $$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.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)))) :rule forall_inst :args ((:= X tptp.identity) (:= Y tptp.a) (:= Z tptp.a)))
% 18.60/18.83  (step t264.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) :rule or :premises (t264.t1))
% 18.60/18.83  (step t264.t3 (cl (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) :rule resolution :premises (t264.t2 t264.a0))
% 18.60/18.83  (step t264 (cl (not (forall ((X $$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.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) :rule subproof :discharge (t264.a0))
% 18.60/18.83  (step t265 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) :rule resolution :premises (t263 t264))
% 18.60/18.83  (step t266 (cl (=> (forall ((X $$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.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)))) :rule implies_neg2)
% 18.60/18.83  (step t267 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) (=> (forall ((X $$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.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)))) :rule resolution :premises (t265 t266))
% 18.60/18.83  (step t268 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z))) (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a)))) :rule contraction :premises (t267))
% 18.60/18.83  (step t269 (cl (not (forall ((X $$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.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) :rule implies :premises (t268))
% 18.60/18.83  (step t270 (cl (= (tptp.greatest_lower_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.a)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.a))) :rule resolution :premises (t269 a5))
% 18.60/18.83  (step t271 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) :rule implies_neg1)
% 18.60/18.83  (anchor :step t272)
% 18.60/18.83  (assume t272.a0 (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))))
% 18.60/18.83  (step t272.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule forall_inst :args ((:= X (tptp.greatest_lower_bound tptp.a tptp.identity))))
% 18.60/18.83  (step t272.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule or :premises (t272.t1))
% 18.60/18.83  (step t272.t3 (cl (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule resolution :premises (t272.t2 t272.a0))
% 18.60/18.83  (step t272 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule subproof :discharge (t272.a0))
% 18.60/18.83  (step t273 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule resolution :premises (t271 t272))
% 18.60/18.83  (step t274 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule implies_neg2)
% 18.60/18.83  (step t275 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule resolution :premises (t273 t274))
% 18.60/18.83  (step t276 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule contraction :premises (t275))
% 18.60/18.83  (step t277 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule implies :premises (t276))
% 18.60/18.83  (step t278 (cl (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule resolution :premises (t277 t166))
% 18.60/18.83  (step t279 (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.a)))) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) :rule implies_neg1)
% 18.60/18.83  (anchor :step t280)
% 18.60/18.83  (assume t280.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))))
% 18.60/18.83  (step t280.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.a))))) :rule forall_inst :args ((:= X tptp.identity) (:= Y tptp.a)))
% 18.60/18.83  (step t280.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.a)))) :rule or :premises (t280.t1))
% 18.60/18.83  (step t280.t3 (cl (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) :rule resolution :premises (t280.t2 t280.a0))
% 18.60/18.83  (step t280 (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.a)))) :rule subproof :discharge (t280.a0))
% 18.60/18.83  (step t281 (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.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) :rule resolution :premises (t279 t280))
% 18.60/18.83  (step t282 (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.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) :rule implies_neg2)
% 18.60/18.83  (step t283 (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.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.a))))) :rule resolution :premises (t281 t282))
% 18.60/18.83  (step t284 (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.a))))) :rule contraction :premises (t283))
% 18.60/18.83  (step t285 (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.a)))) :rule implies :premises (t284))
% 18.60/18.83  (step t286 (cl (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) :rule resolution :premises (t285 t261))
% 18.60/18.83  (step t287 (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)
% 18.60/18.83  (anchor :step t288)
% 18.60/18.83  (assume t288.a0 (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))))
% 18.60/18.83  (step t288.t1 (cl (or (not (forall ((X $$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))))
% 18.60/18.83  (step t288.t2 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule or :premises (t288.t1))
% 18.60/18.83  (step t288.t3 (cl (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule resolution :premises (t288.t2 t288.a0))
% 18.60/18.83  (step t288 (cl (not (forall ((X $$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 (t288.a0))
% 18.60/18.83  (step t289 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule resolution :premises (t287 t288))
% 18.60/18.83  (step t290 (cl (=> (forall ((X $$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)
% 18.60/18.83  (step t291 (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 (t289 t290))
% 18.60/18.83  (step t292 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule contraction :premises (t291))
% 18.60/18.83  (step t293 (cl (not (forall ((X $$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 (t292))
% 18.60/18.83  (step t294 (cl (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule resolution :premises (t293 t177))
% 18.60/18.83  (step t295 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) :rule implies_neg1)
% 18.60/18.83  (anchor :step t296)
% 18.60/18.83  (assume t296.a0 (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))))
% 18.60/18.83  (step t296.t1 (cl (or (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule forall_inst :args ((:= X (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))))
% 18.60/18.83  (step t296.t2 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) :rule or :premises (t296.t1))
% 18.60/18.83  (step t296.t3 (cl (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) :rule resolution :premises (t296.t2 t296.a0))
% 18.60/18.83  (step t296 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) :rule subproof :discharge (t296.a0))
% 18.60/18.83  (step t297 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) :rule resolution :premises (t295 t296))
% 18.60/18.83  (step t298 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule implies_neg2)
% 18.60/18.83  (step t299 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule resolution :premises (t297 t298))
% 18.60/18.83  (step t300 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule contraction :premises (t299))
% 18.60/18.83  (step t301 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) :rule implies :premises (t300))
% 18.60/18.83  (step t302 (cl (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))))) :rule resolution :premises (t301 t177))
% 18.60/18.83  (step t303 (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.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) :rule implies_neg1)
% 18.60/18.83  (anchor :step t304)
% 18.60/18.83  (assume t304.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))))
% 18.60/18.83  (step t304.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.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)))) :rule forall_inst :args ((:= X tptp.a) (:= Y (tptp.multiply tptp.a tptp.a))))
% 18.60/18.83  (step t304.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.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) :rule or :premises (t304.t1))
% 18.60/18.83  (step t304.t3 (cl (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) :rule resolution :premises (t304.t2 t304.a0))
% 18.60/18.83  (step t304 (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.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) :rule subproof :discharge (t304.a0))
% 18.60/18.83  (step t305 (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.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) :rule resolution :premises (t303 t304))
% 18.60/18.83  (step t306 (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.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)))) :rule implies_neg2)
% 18.60/18.83  (step t307 (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.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) 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.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)))) :rule resolution :premises (t305 t306))
% 18.60/18.83  (step t308 (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.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a)))) :rule contraction :premises (t307))
% 18.60/18.83  (step t309 (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.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) :rule implies :premises (t308))
% 18.60/18.83  (step t310 (cl (= (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) tptp.a))) :rule resolution :premises (t309 a4))
% 18.60/18.83  (step t311 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (forall ((Y $$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)
% 18.60/18.83  (anchor :step t312)
% 18.60/18.83  (assume t312.a0 (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))))
% 18.60/18.83  (step t312.t1 (cl (or (not (forall ((Y $$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.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))))) :rule forall_inst :args ((:= Y tptp.a) (:= Z tptp.identity) (:= X tptp.a)))
% 18.60/18.83  (step t312.t2 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) :rule or :premises (t312.t1))
% 18.60/18.83  (step t312.t3 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) :rule resolution :premises (t312.t2 t312.a0))
% 18.60/18.83  (step t312 (cl (not (forall ((Y $$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.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) :rule subproof :discharge (t312.a0))
% 18.60/18.83  (step t313 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) :rule resolution :premises (t311 t312))
% 18.60/18.83  (step t314 (cl (=> (forall ((Y $$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.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))))) :rule implies_neg2)
% 18.60/18.83  (step t315 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) (=> (forall ((Y $$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.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))))) :rule resolution :premises (t313 t314))
% 18.60/18.83  (step t316 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a))))) :rule contraction :premises (t315))
% 18.60/18.83  (step t317 (cl (not (forall ((Y $$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.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) :rule implies :premises (t316))
% 18.60/18.83  (step t318 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.identity tptp.a)))) :rule resolution :premises (t317 a13))
% 18.60/18.83  (step t319 (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.multiply tptp.a tptp.a))))) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) :rule implies_neg1)
% 18.60/18.83  (anchor :step t320)
% 18.60/18.83  (assume t320.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))))
% 18.60/18.83  (step t320.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.multiply tptp.a tptp.a)))))) :rule forall_inst :args ((:= X tptp.a) (:= Y (tptp.multiply tptp.a tptp.a))))
% 18.60/18.83  (step t320.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.multiply tptp.a tptp.a))))) :rule or :premises (t320.t1))
% 18.60/18.83  (step t320.t3 (cl (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) :rule resolution :premises (t320.t2 t320.a0))
% 18.60/18.83  (step t320 (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.multiply tptp.a tptp.a))))) :rule subproof :discharge (t320.a0))
% 18.60/18.83  (step t321 (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.multiply tptp.a tptp.a))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) :rule resolution :premises (t319 t320))
% 18.60/18.83  (step t322 (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.multiply tptp.a tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a)))))) :rule implies_neg2)
% 18.60/18.83  (step t323 (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.multiply tptp.a tptp.a))))) (=> (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.multiply tptp.a tptp.a)))))) :rule resolution :premises (t321 t322))
% 18.60/18.83  (step t324 (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.multiply tptp.a tptp.a)))))) :rule contraction :premises (t323))
% 18.60/18.83  (step t325 (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.multiply tptp.a tptp.a))))) :rule implies :premises (t324))
% 18.60/18.83  (step t326 (cl (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.multiply tptp.a tptp.a))))) :rule resolution :premises (t325 t218))
% 18.60/18.83  (step t327 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 18.60/18.83  (anchor :step t328)
% 18.60/18.83  (assume t328.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 18.60/18.83  (step t328.t1 (cl (or (not (forall ((X $$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.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule forall_inst :args ((:= X (tptp.inverse (tptp.inverse tptp.a))) (:= Y (tptp.inverse tptp.a)) (:= Z tptp.a)))
% 18.60/18.83  (step t328.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule or :premises (t328.t1))
% 18.60/18.83  (step t328.t3 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule resolution :premises (t328.t2 t328.a0))
% 18.60/18.83  (step t328 (cl (not (forall ((X $$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.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule subproof :discharge (t328.a0))
% 18.60/18.83  (step t329 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule resolution :premises (t327 t328))
% 18.60/18.83  (step t330 (cl (=> (forall ((X $$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.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule implies_neg2)
% 18.60/18.83  (step t331 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (=> (forall ((X $$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.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule resolution :premises (t329 t330))
% 18.60/18.83  (step t332 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule contraction :premises (t331))
% 18.60/18.83  (step t333 (cl (not (forall ((X $$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.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule implies :premises (t332))
% 18.60/18.83  (step t334 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule resolution :premises (t333 a2))
% 18.60/18.83  (step t335 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (forall ((X $$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)
% 18.60/18.83  (anchor :step t336)
% 18.60/18.83  (assume t336.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))))
% 18.60/18.83  (step t336.t1 (cl (or (not (forall ((X $$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.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))))) :rule forall_inst :args ((:= X tptp.a) (:= Y tptp.a) (:= Z tptp.identity)))
% 18.60/18.83  (step t336.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) :rule or :premises (t336.t1))
% 18.60/18.83  (step t336.t3 (cl (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) :rule resolution :premises (t336.t2 t336.a0))
% 18.60/18.83  (step t336 (cl (not (forall ((X $$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.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) :rule subproof :discharge (t336.a0))
% 18.60/18.83  (step t337 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) :rule resolution :premises (t335 t336))
% 18.60/18.83  (step t338 (cl (=> (forall ((X $$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.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))))) :rule implies_neg2)
% 18.60/18.83  (step t339 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) (=> (forall ((X $$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.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))))) :rule resolution :premises (t337 t338))
% 18.60/18.83  (step t340 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity))))) :rule contraction :premises (t339))
% 18.60/18.83  (step t341 (cl (not (forall ((X $$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.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) :rule implies :premises (t340))
% 18.60/18.83  (step t342 (cl (= (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.a) (tptp.multiply tptp.a tptp.identity)))) :rule resolution :premises (t341 a11))
% 18.60/18.83  (step t343 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) :rule implies_neg1)
% 18.60/18.83  (anchor :step t344)
% 18.60/18.83  (assume t344.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))))
% 18.60/18.83  (step t344.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule forall_inst :args ((:= X (tptp.greatest_lower_bound tptp.a tptp.identity)) (:= Y tptp.identity)))
% 18.60/18.83  (step t344.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule or :premises (t344.t1))
% 18.60/18.83  (step t344.t3 (cl (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule resolution :premises (t344.t2 t344.a0))
% 18.60/18.83  (step t344 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule subproof :discharge (t344.a0))
% 18.60/18.83  (step t345 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule resolution :premises (t343 t344))
% 18.60/18.83  (step t346 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule implies_neg2)
% 18.60/18.83  (step t347 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound 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.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule resolution :premises (t345 t346))
% 18.60/18.83  (step t348 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule contraction :premises (t347))
% 18.60/18.83  (step t349 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule implies :premises (t348))
% 18.60/18.83  (step t350 (cl (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule resolution :premises (t349 a4))
% 18.60/18.83  (step t351 (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.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_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)
% 18.60/18.83  (anchor :step t352)
% 18.60/18.83  (assume t352.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))))
% 18.60/18.83  (step t352.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.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) :rule forall_inst :args ((:= X tptp.a) (:= Y (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))))
% 18.60/18.83  (step t352.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.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) :rule or :premises (t352.t1))
% 18.60/18.83  (step t352.t3 (cl (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) :rule resolution :premises (t352.t2 t352.a0))
% 18.60/18.83  (step t352 (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.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) :rule subproof :discharge (t352.a0))
% 18.60/18.83  (step t353 (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.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) :rule resolution :premises (t351 t352))
% 18.60/18.83  (step t354 (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.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) :rule implies_neg2)
% 18.60/18.83  (step t355 (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.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_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.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) :rule resolution :premises (t353 t354))
% 18.60/18.83  (step t356 (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.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) :rule contraction :premises (t355))
% 18.60/18.83  (step t357 (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.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) :rule implies :premises (t356))
% 18.60/18.83  (step t358 (cl (= (tptp.greatest_lower_bound tptp.a (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) :rule resolution :premises (t357 a3))
% 18.60/18.83  (step t359 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) :rule implies_neg1)
% 18.60/18.83  (anchor :step t360)
% 18.60/18.83  (assume t360.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))))
% 18.60/18.83  (step t360.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))))) :rule forall_inst :args ((:= X (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (:= Y tptp.a)))
% 18.60/18.83  (step t360.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) :rule or :premises (t360.t1))
% 18.60/18.83  (step t360.t3 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) :rule resolution :premises (t360.t2 t360.a0))
% 18.60/18.83  (step t360 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) :rule subproof :discharge (t360.a0))
% 18.60/18.83  (step t361 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) :rule resolution :premises (t359 t360))
% 18.60/18.83  (step t362 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))))) :rule implies_neg2)
% 18.60/18.83  (step t363 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))))) :rule resolution :premises (t361 t362))
% 18.60/18.83  (step t364 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))))) :rule contraction :premises (t363))
% 18.60/18.83  (step t365 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) :rule implies :premises (t364))
% 18.60/18.83  (step t366 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) :rule resolution :premises (t365 t261))
% 18.60/18.83  (step t367 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 18.60/18.83  (anchor :step t368)
% 18.60/18.83  (assume t368.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 18.60/18.83  (step t368.t1 (cl (or (not (forall ((X $$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.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule forall_inst :args ((:= X (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)))) (:= Y (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (:= Z (tptp.least_upper_bound tptp.a tptp.identity))))
% 18.60/18.83  (step t368.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule or :premises (t368.t1))
% 18.60/18.83  (step t368.t3 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule resolution :premises (t368.t2 t368.a0))
% 18.60/18.83  (step t368 (cl (not (forall ((X $$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.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule subproof :discharge (t368.a0))
% 18.60/18.83  (step t369 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule resolution :premises (t367 t368))
% 18.60/18.83  (step t370 (cl (=> (forall ((X $$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.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule implies_neg2)
% 18.60/18.83  (step t371 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (=> (forall ((X $$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.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule resolution :premises (t369 t370))
% 18.60/18.83  (step t372 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule contraction :premises (t371))
% 18.60/18.83  (step t373 (cl (not (forall ((X $$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.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule implies :premises (t372))
% 18.60/18.83  (step t374 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule resolution :premises (t373 a2))
% 18.60/18.83  (step t375 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (forall ((X $$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)
% 18.60/18.83  (anchor :step t376)
% 18.60/18.83  (assume t376.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))))
% 18.60/18.83  (step t376.t1 (cl (or (not (forall ((X $$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.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))))) :rule forall_inst :args ((:= X (tptp.least_upper_bound tptp.a tptp.identity)) (:= Y tptp.a) (:= Z tptp.identity)))
% 18.60/18.83  (step t376.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) :rule or :premises (t376.t1))
% 18.60/18.83  (step t376.t3 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) :rule resolution :premises (t376.t2 t376.a0))
% 18.60/18.83  (step t376 (cl (not (forall ((X $$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.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) :rule subproof :discharge (t376.a0))
% 18.60/18.83  (step t377 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) :rule resolution :premises (t375 t376))
% 18.60/18.83  (step t378 (cl (=> (forall ((X $$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.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))))) :rule implies_neg2)
% 18.60/18.83  (step t379 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) (=> (forall ((X $$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.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))))) :rule resolution :premises (t377 t378))
% 18.60/18.83  (step t380 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity))))) :rule contraction :premises (t379))
% 18.60/18.83  (step t381 (cl (not (forall ((X $$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.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) :rule implies :premises (t380))
% 18.60/18.83  (step t382 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.identity)))) :rule resolution :premises (t381 a12))
% 18.60/18.83  (step t383 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (forall ((X $$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)
% 18.60/18.83  (anchor :step t384)
% 18.60/18.83  (assume t384.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z))))
% 18.60/18.83  (step t384.t1 (cl (or (not (forall ((X $$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.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule forall_inst :args ((:= X (tptp.greatest_lower_bound tptp.a tptp.a)) (:= Y (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (:= Z (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))))
% 18.60/18.83  (step t384.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) :rule or :premises (t384.t1))
% 18.60/18.83  (step t384.t3 (cl (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) :rule resolution :premises (t384.t2 t384.a0))
% 18.60/18.83  (step t384 (cl (not (forall ((X $$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.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) :rule subproof :discharge (t384.a0))
% 18.60/18.83  (step t385 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) :rule resolution :premises (t383 t384))
% 18.60/18.83  (step t386 (cl (=> (forall ((X $$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.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule implies_neg2)
% 18.60/18.83  (step t387 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) (=> (forall ((X $$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.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule resolution :premises (t385 t386))
% 18.60/18.83  (step t388 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule contraction :premises (t387))
% 18.60/18.83  (step t389 (cl (not (forall ((X $$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.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) :rule implies :premises (t388))
% 18.60/18.83  (step t390 (cl (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.multiply tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.least_upper_bound tptp.a tptp.identity))))) :rule resolution :premises (t389 a5))
% 18.60/18.83  (step t391 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (forall ((X $$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)
% 18.60/18.83  (anchor :step t392)
% 18.60/18.83  (assume t392.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))))
% 18.60/18.83  (step t392.t1 (cl (or (not (forall ((X $$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.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))))) :rule forall_inst :args ((:= X tptp.a) (:= Y (tptp.greatest_lower_bound tptp.a tptp.identity)) (:= Z tptp.identity)))
% 18.60/18.83  (step t392.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) :rule or :premises (t392.t1))
% 18.60/18.83  (step t392.t3 (cl (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) :rule resolution :premises (t392.t2 t392.a0))
% 18.60/18.83  (step t392 (cl (not (forall ((X $$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.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) :rule subproof :discharge (t392.a0))
% 18.60/18.83  (step t393 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) :rule resolution :premises (t391 t392))
% 18.60/18.83  (step t394 (cl (=> (forall ((X $$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.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))))) :rule implies_neg2)
% 18.60/18.83  (step t395 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) (=> (forall ((X $$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.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))))) :rule resolution :premises (t393 t394))
% 18.60/18.83  (step t396 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity))))) :rule contraction :premises (t395))
% 18.60/18.83  (step t397 (cl (not (forall ((X $$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.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) :rule implies :premises (t396))
% 18.60/18.83  (step t398 (cl (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) :rule resolution :premises (t397 a11))
% 18.60/18.83  (step t399 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (forall ((Y $$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)
% 18.60/18.83  (anchor :step t400)
% 18.60/18.83  (assume t400.a0 (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))))
% 18.60/18.83  (step t400.t1 (cl (or (not (forall ((Y $$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.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule forall_inst :args ((:= Y tptp.a) (:= Z tptp.identity) (:= X (tptp.greatest_lower_bound tptp.a tptp.identity))))
% 18.60/18.83  (step t400.t2 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule or :premises (t400.t1))
% 18.60/18.83  (step t400.t3 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule resolution :premises (t400.t2 t400.a0))
% 18.60/18.83  (step t400 (cl (not (forall ((Y $$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.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule subproof :discharge (t400.a0))
% 18.60/18.83  (step t401 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule resolution :premises (t399 t400))
% 18.60/18.83  (step t402 (cl (=> (forall ((Y $$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.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule implies_neg2)
% 18.60/18.83  (step t403 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (=> (forall ((Y $$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.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule resolution :premises (t401 t402))
% 18.60/18.83  (step t404 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule contraction :premises (t403))
% 18.60/18.83  (step t405 (cl (not (forall ((Y $$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.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule implies :premises (t404))
% 18.60/18.83  (step t406 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule resolution :premises (t405 a13))
% 18.60/18.83  (step t407 (cl (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)))) :rule resolution :premises (t132 a18 t145 t156 t167 t178 t189 t200 t208 t219 t227 t235 t243 t251 t262 t270 t278 t286 t294 t302 t310 t318 t326 t334 t342 t350 t358 t366 t374 t382 t390 t398 t406))
% 18.60/18.83  (step t408 (cl) :rule resolution :premises (t7 t407 a6))
% 18.60/18.83  
% 18.60/18.83  % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.jkiYFG9902/cvc5---1.0.5_29032.smt2
% 18.60/18.84  % cvc5---1.0.5 exiting
% 18.60/18.84  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------