%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : GRP179-2 : TPTP v8.2.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : do_cvc5 %s %d

% Computer : n005.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed May 29 16:53:34 EDT 2024

% Result   : Unsatisfiable 54.12s 54.35s
% Output   : Proof 54.31s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : GRP179-2 : TPTP v8.2.0. Bugfixed v1.2.1.
% 0.11/0.13  % Command    : do_cvc5 %s %d
% 0.14/0.34  % Computer : n005.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Sun May 26 19:56:09 EDT 2024
% 0.14/0.34  % CPUTime    : 
% 0.21/0.49  %----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...
% 10.60/10.80  --- Run --no-e-matching --full-saturate-quant at 5...
% 15.61/15.85  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 20.68/20.89  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 25.69/25.93  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 30.81/31.04  --- Run --trigger-sel=max --full-saturate-quant at 5...
% 35.90/36.12  --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 41.02/41.23  --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 46.10/46.34  --- Run --prenex-quant=none --full-saturate-quant at 5...
% 51.22/51.45  --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 54.12/54.35  % SZS status Unsatisfiable for /export/starexec/sandbox2/tmp/tmp.cyo0oJjqrY/cvc5---1.0.5_25890.smt2
% 54.12/54.35  % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.cyo0oJjqrY/cvc5---1.0.5_25890.smt2
% 54.31/54.53  (assume a0 (forall ((X $$unsorted)) (= (tptp.multiply tptp.identity X) X)))
% 54.31/54.53  (assume a1 (forall ((X $$unsorted)) (= (tptp.multiply (tptp.inverse X) X) tptp.identity)))
% 54.31/54.53  (assume a2 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 54.31/54.53  (assume a3 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))))
% 54.31/54.53  (assume a4 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))))
% 54.31/54.53  (assume a5 (forall ((X $$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))))
% 54.31/54.53  (assume a6 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))))
% 54.31/54.53  (assume a7 (forall ((X $$unsorted)) (= (tptp.least_upper_bound X X) X)))
% 54.31/54.53  (assume a8 (forall ((X $$unsorted)) (= (tptp.greatest_lower_bound X X) X)))
% 54.31/54.53  (assume a9 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)) X)))
% 54.31/54.53  (assume a10 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)) X)))
% 54.31/54.53  (assume a11 (forall ((X $$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)))))
% 54.31/54.53  (assume a12 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))))
% 54.31/54.53  (assume a13 (forall ((Y $$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)))))
% 54.31/54.53  (assume a14 (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))))
% 54.31/54.53  (assume a15 (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))
% 54.31/54.53  (step t1 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 54.31/54.53  (anchor :step t2)
% 54.31/54.53  (assume t2.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 54.31/54.53  (step t2.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) :rule forall_inst :args ((:= X (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (:= Y (tptp.greatest_lower_bound tptp.identity tptp.a)) (:= Z (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))
% 54.31/54.53  (step t2.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule or :premises (t2.t1))
% 54.31/54.53  (step t2.t3 (cl (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule resolution :premises (t2.t2 t2.a0))
% 54.31/54.53  (step t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule subproof :discharge (t2.a0))
% 54.31/54.53  (step t3 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule resolution :premises (t1 t2))
% 54.31/54.53  (step t4 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) :rule implies_neg2)
% 54.31/54.53  (step t5 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) :rule resolution :premises (t3 t4))
% 54.31/54.53  (step t6 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) :rule contraction :premises (t5))
% 54.31/54.53  (step t7 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule implies :premises (t6))
% 54.31/54.53  (step t8 (cl (not (= (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))))) (not (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))))) (or (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))))) :rule equiv_pos2)
% 54.31/54.53  (step t9 (cl (= (= (= (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) true) (= (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule equiv_simplify)
% 54.31/54.53  (step t10 (cl (not (= (= (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) true)) (= (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule equiv1 :premises (t9))
% 54.31/54.53  (step t11 (cl (= (= (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))))) :rule all_simplify)
% 54.31/54.53  (step t12 (cl (= (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule refl)
% 54.31/54.53  (step t13 (cl (= (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule all_simplify)
% 54.31/54.53  (step t14 (cl (= (= (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule cong :premises (t12 t13))
% 54.31/54.53  (step t15 (cl (= (= (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) true)) :rule all_simplify)
% 54.31/54.53  (step t16 (cl (= (= (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) true)) :rule trans :premises (t14 t15))
% 54.31/54.53  (step t17 (cl (= (= (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) true)) :rule trans :premises (t11 t16))
% 54.31/54.53  (step t18 (cl (= (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule resolution :premises (t10 t17))
% 54.31/54.53  (step t19 (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)
% 54.31/54.53  (step t20 (cl (= (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule refl)
% 54.31/54.53  (step t21 (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)
% 54.31/54.53  (step t22 (cl (= (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))))) :rule refl)
% 54.31/54.53  (step t23 (cl (= (not (= tptp.a (tptp.least_upper_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.identity)))))) :rule refl)
% 54.31/54.53  (step t24 (cl (= (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))))) :rule refl)
% 54.31/54.53  (step t25 (cl (= (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))))) :rule refl)
% 54.31/54.53  (step t26 (cl (= (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))))) :rule refl)
% 54.31/54.53  (step t27 (cl (= (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))))) :rule refl)
% 54.31/54.53  (step t28 (cl (= (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))))) :rule refl)
% 54.31/54.53  (step t29 (cl (= (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))))) :rule refl)
% 54.31/54.53  (step t30 (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)
% 54.31/54.53  (step t31 (cl (= (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))))) :rule refl)
% 54.31/54.53  (step t32 (cl (= (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))))) :rule refl)
% 54.31/54.53  (step t33 (cl (= (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))))) :rule refl)
% 54.31/54.53  (step t34 (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)
% 54.31/54.53  (step t35 (cl (= (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))))) :rule refl)
% 54.31/54.53  (step t36 (cl (= (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))))) :rule refl)
% 54.31/54.53  (step t37 (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)
% 54.31/54.53  (step t38 (cl (= (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))))) :rule refl)
% 54.31/54.53  (step t39 (cl (= (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule refl)
% 54.31/54.53  (step t40 (cl (= (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))))) :rule refl)
% 54.31/54.53  (step t41 (cl (= (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule refl)
% 54.31/54.53  (step t42 (cl (= (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) :rule refl)
% 54.31/54.53  (step t43 (cl (= (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))))) :rule refl)
% 54.31/54.53  (step t44 (cl (= (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))))) :rule refl)
% 54.31/54.53  (step t45 (cl (= (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))))) :rule refl)
% 54.31/54.53  (step t46 (cl (= (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))))) :rule refl)
% 54.31/54.53  (step t47 (cl (= (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule refl)
% 54.31/54.53  (step t48 (cl (= (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))))) :rule refl)
% 54.31/54.53  (step t49 (cl (= (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))))) :rule refl)
% 54.31/54.53  (step t50 (cl (= (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))))) :rule refl)
% 54.31/54.53  (step t51 (cl (= (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))))) :rule refl)
% 54.31/54.53  (step t52 (cl (= (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))))) :rule refl)
% 54.31/54.53  (step t53 (cl (= (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))))) :rule refl)
% 54.31/54.53  (step t54 (cl (= (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))))) :rule refl)
% 54.31/54.53  (step t55 (cl (= (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))))) :rule refl)
% 54.31/54.53  (step t56 (cl (= (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule refl)
% 54.31/54.53  (step t57 (cl (= (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))))) :rule refl)
% 54.31/54.53  (step t58 (cl (= (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) :rule refl)
% 54.31/54.53  (step t59 (cl (= (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) :rule refl)
% 54.31/54.53  (step t60 (cl (= (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))))) :rule refl)
% 54.31/54.53  (step t61 (cl (= (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))))) :rule refl)
% 54.31/54.53  (step t62 (cl (= (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))))) :rule refl)
% 54.31/54.53  (step t63 (cl (= (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))))) :rule refl)
% 54.31/54.53  (step t64 (cl (= (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))))) :rule refl)
% 54.31/54.53  (step t65 (cl (= (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))))) :rule refl)
% 54.31/54.53  (step t66 (cl (= (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))))) :rule refl)
% 54.31/54.53  (step t67 (cl (= (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))))) :rule refl)
% 54.31/54.53  (step t68 (cl (= (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))))) :rule refl)
% 54.31/54.53  (step t69 (cl (= (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))))) :rule refl)
% 54.31/54.53  (step t70 (cl (= (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))))) :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 t51 t52 t53 t54 t55 t56 t57 t58 t59 t60 t61 t62 t63 t64 t65 t66 t67 t68 t69))
% 54.31/54.53  (step t71 (cl (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) :rule and_neg)
% 54.31/54.53  (step t72 (cl (=> (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) :rule implies_neg1)
% 54.31/54.53  (anchor :step t73)
% 54.31/54.53  (assume t73.a0 (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))
% 54.31/54.53  (assume t73.a1 (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))
% 54.31/54.53  (assume t73.a2 (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))))
% 54.31/54.53  (assume t73.a3 (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))
% 54.31/54.53  (assume t73.a4 (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))
% 54.31/54.53  (assume t73.a5 (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))
% 54.31/54.53  (assume t73.a6 (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))
% 54.31/54.53  (assume t73.a7 (= tptp.identity (tptp.multiply tptp.identity tptp.identity)))
% 54.31/54.53  (assume t73.a8 (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)))
% 54.31/54.53  (assume t73.a9 (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)))
% 54.31/54.53  (assume t73.a10 (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)))
% 54.31/54.53  (assume t73.a11 (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))))
% 54.31/54.53  (assume t73.a12 (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))
% 54.31/54.53  (assume t73.a13 (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))))
% 54.31/54.53  (assume t73.a14 (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))))
% 54.31/54.53  (assume t73.a15 (= tptp.a (tptp.multiply tptp.identity tptp.a)))
% 54.31/54.53  (assume t73.a16 (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))
% 54.31/54.53  (assume t73.a17 (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))))
% 54.31/54.53  (assume t73.a18 (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)))
% 54.31/54.53  (assume t73.a19 (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))
% 54.31/54.53  (assume t73.a20 (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))))
% 54.31/54.53  (assume t73.a21 (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))
% 54.31/54.53  (assume t73.a22 (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))))
% 54.31/54.53  (assume t73.a23 (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))
% 54.31/54.53  (assume t73.a24 (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))))
% 54.31/54.53  (assume t73.a25 (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))))
% 54.31/54.53  (assume t73.a26 (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))))
% 54.31/54.53  (assume t73.a27 (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))
% 54.31/54.53  (assume t73.a28 (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))
% 54.31/54.53  (assume t73.a29 (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))))
% 54.31/54.53  (assume t73.a30 (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))))
% 54.31/54.53  (assume t73.a31 (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))
% 54.31/54.53  (assume t73.a32 (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))
% 54.31/54.53  (assume t73.a33 (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))))
% 54.31/54.53  (assume t73.a34 (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))))
% 54.31/54.53  (assume t73.a35 (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))))
% 54.31/54.53  (assume t73.a36 (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))))
% 54.31/54.53  (assume t73.a37 (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))))
% 54.31/54.53  (assume t73.a38 (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))
% 54.31/54.53  (assume t73.a39 (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))))
% 54.31/54.53  (assume t73.a40 (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))
% 54.31/54.53  (assume t73.a41 (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))
% 54.31/54.53  (assume t73.a42 (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))
% 54.31/54.53  (assume t73.a43 (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))
% 54.31/54.53  (assume t73.a44 (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))))
% 54.31/54.53  (assume t73.a45 (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))))
% 54.31/54.53  (assume t73.a46 (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))
% 54.31/54.53  (assume t73.a47 (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))))
% 54.31/54.53  (assume t73.a48 (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))))
% 54.31/54.53  (assume t73.a49 (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))
% 54.31/54.53  (assume t73.a50 (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))
% 54.31/54.53  (step t73.t1 (cl (=> (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule implies_neg1)
% 54.31/54.53  (anchor :step t73.t2)
% 54.31/54.53  (assume t73.t2.a0 (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)))
% 54.31/54.53  (assume t73.t2.a1 (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))
% 54.31/54.53  (assume t73.t2.a2 (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))
% 54.31/54.53  (assume t73.t2.a3 (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))
% 54.31/54.53  (assume t73.t2.a4 (= tptp.a (tptp.multiply tptp.identity tptp.a)))
% 54.31/54.53  (assume t73.t2.a5 (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))
% 54.31/54.53  (assume t73.t2.a6 (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))
% 54.31/54.53  (assume t73.t2.a7 (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))))
% 54.31/54.53  (assume t73.t2.a8 (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))
% 54.31/54.53  (assume t73.t2.a9 (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))))
% 54.31/54.53  (assume t73.t2.a10 (= tptp.identity (tptp.multiply tptp.identity tptp.identity)))
% 54.31/54.53  (assume t73.t2.a11 (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))))
% 54.31/54.53  (assume t73.t2.a12 (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))
% 54.31/54.53  (assume t73.t2.a13 (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))))
% 54.31/54.53  (assume t73.t2.a14 (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))))
% 54.31/54.53  (assume t73.t2.a15 (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))))
% 54.31/54.53  (assume t73.t2.a16 (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)))
% 54.31/54.53  (assume t73.t2.a17 (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))
% 54.31/54.53  (assume t73.t2.a18 (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))
% 54.31/54.53  (assume t73.t2.a19 (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)))
% 54.31/54.53  (assume t73.t2.a20 (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))))
% 54.31/54.53  (assume t73.t2.a21 (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))))
% 54.31/54.53  (assume t73.t2.a22 (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))
% 54.31/54.53  (assume t73.t2.a23 (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))))
% 54.31/54.53  (assume t73.t2.a24 (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))))
% 54.31/54.53  (assume t73.t2.a25 (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))))
% 54.31/54.53  (assume t73.t2.a26 (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))))
% 54.31/54.53  (assume t73.t2.a27 (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))))
% 54.31/54.53  (assume t73.t2.a28 (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))
% 54.31/54.53  (assume t73.t2.a29 (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))
% 54.31/54.53  (assume t73.t2.a30 (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))
% 54.31/54.53  (assume t73.t2.a31 (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))))
% 54.31/54.53  (assume t73.t2.a32 (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))))
% 54.31/54.53  (assume t73.t2.a33 (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))
% 54.31/54.53  (assume t73.t2.a34 (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))
% 54.31/54.53  (assume t73.t2.a35 (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))))
% 54.31/54.53  (assume t73.t2.a36 (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))))
% 54.31/54.53  (assume t73.t2.a37 (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))))
% 54.31/54.53  (assume t73.t2.a38 (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))
% 54.31/54.53  (assume t73.t2.a39 (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)))
% 54.31/54.53  (assume t73.t2.a40 (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))))
% 54.31/54.53  (assume t73.t2.a41 (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))
% 54.31/54.53  (assume t73.t2.a42 (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))))
% 54.31/54.53  (assume t73.t2.a43 (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))
% 54.31/54.53  (assume t73.t2.a44 (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))
% 54.31/54.53  (assume t73.t2.a45 (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))
% 54.31/54.53  (assume t73.t2.a46 (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))
% 54.31/54.53  (assume t73.t2.a47 (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))))
% 54.31/54.53  (assume t73.t2.a48 (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))
% 54.31/54.53  (assume t73.t2.a49 (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))))
% 54.31/54.53  (assume t73.t2.a50 (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))
% 54.31/54.53  (step t73.t2.t1 (cl (= (= (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) false) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))))) :rule equiv_simplify)
% 54.31/54.53  (step t73.t2.t2 (cl (not (= (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) false)) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) :rule equiv1 :premises (t73.t2.t1))
% 54.31/54.53  (step t73.t2.t3 (cl (not (= (= (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) false) (= (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) false))) (not (= (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) false)) (= (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) false)) :rule equiv_pos2)
% 54.31/54.53  (step t73.t2.t4 (cl (= (= (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) false) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) :rule all_simplify)
% 54.31/54.53  (step t73.t2.t5 (cl (= (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) :rule all_simplify)
% 54.31/54.53  (step t73.t2.t6 (cl (= (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))))) :rule cong :premises (t73.t2.t5))
% 54.31/54.53  (step t73.t2.t7 (cl (= (= (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) false) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))))) :rule trans :premises (t73.t2.t4 t73.t2.t6))
% 54.31/54.53  (step t73.t2.t8 (cl (= (= (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) false) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))))) :rule all_simplify)
% 54.31/54.53  (step t73.t2.t9 (cl (= (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) false))) :rule symm :premises (t73.t2.t8))
% 54.31/54.53  (step t73.t2.t10 (cl (= (= (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) false) (= (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) false))) :rule trans :premises (t73.t2.t7 t73.t2.t9))
% 54.31/54.53  (step t73.t2.t11 (cl (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule refl)
% 54.31/54.53  (step t73.t2.t12 (cl (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.inverse tptp.a))) :rule symm :premises (t73.t2.a43))
% 54.31/54.53  (step t73.t2.t13 (cl (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule symm :premises (t73.t2.t12))
% 54.31/54.53  (step t73.t2.t14 (cl (= (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule symm :premises (t73.t2.a42))
% 54.31/54.53  (step t73.t2.t15 (cl (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) :rule symm :premises (t73.t2.t14))
% 54.31/54.53  (step t73.t2.t16 (cl (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) :rule trans :premises (t73.t2.t13 t73.t2.t15))
% 54.31/54.53  (step t73.t2.t17 (cl (= tptp.a tptp.a)) :rule refl)
% 54.31/54.53  (step t73.t2.t18 (cl (= (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a))) :rule cong :premises (t73.t2.t16 t73.t2.t17))
% 54.31/54.53  (step t73.t2.t19 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a))) :rule symm :premises (t73.t2.a41))
% 54.31/54.53  (step t73.t2.t20 (cl (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule symm :premises (t73.t2.t19))
% 54.31/54.53  (step t73.t2.t21 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) :rule refl)
% 54.31/54.53  (step t73.t2.t22 (cl (= (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)) :rule symm :premises (t73.t2.a2))
% 54.31/54.53  (step t73.t2.t23 (cl (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) tptp.identity)) :rule symm :premises (t73.t2.a40))
% 54.31/54.53  (step t73.t2.t24 (cl (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) :rule symm :premises (t73.t2.t23))
% 54.31/54.53  (step t73.t2.t25 (cl (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) :rule symm :premises (t73.t2.a39))
% 54.31/54.53  (step t73.t2.t26 (cl (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) :rule symm :premises (t73.t2.t25))
% 54.31/54.53  (step t73.t2.t27 (cl (= (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) :rule symm :premises (t73.t2.a38))
% 54.31/54.53  (step t73.t2.t28 (cl (= tptp.identity tptp.identity)) :rule refl)
% 54.31/54.53  (step t73.t2.t29 (cl (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) :rule cong :premises (t73.t2.t27 t73.t2.t28))
% 54.31/54.53  (step t73.t2.t30 (cl (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) :rule trans :premises (t73.t2.t24 t73.t2.t26 t73.t2.t29))
% 54.31/54.53  (step t73.t2.t31 (cl (= (tptp.multiply tptp.identity tptp.identity) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity))) :rule cong :premises (t73.t2.t30 t73.t2.t28))
% 54.31/54.53  (step t73.t2.t32 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity))) :rule symm :premises (t73.t2.a37))
% 54.31/54.53  (step t73.t2.t33 (cl (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) :rule symm :premises (t73.t2.t32))
% 54.31/54.53  (step t73.t2.t34 (cl (= (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) :rule trans :premises (t73.t2.t22 t73.t2.a10 t73.t2.t31 t73.t2.t33))
% 54.31/54.53  (step t73.t2.t35 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))))) :rule cong :premises (t73.t2.t21 t73.t2.t34))
% 54.31/54.53  (step t73.t2.t36 (cl (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))))) :rule symm :premises (t73.t2.a36))
% 54.31/54.53  (step t73.t2.t37 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) :rule symm :premises (t73.t2.t36))
% 54.31/54.53  (step t73.t2.t38 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule symm :premises (t73.t2.a35))
% 54.31/54.53  (step t73.t2.t39 (cl (= (tptp.multiply tptp.identity tptp.identity) tptp.identity)) :rule symm :premises (t73.t2.a10))
% 54.31/54.53  (step t73.t2.t40 (cl (= (tptp.multiply tptp.identity tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule trans :premises (t73.t2.t39 t73.t2.a2))
% 54.31/54.53  (step t73.t2.t41 (cl (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule cong :premises (t73.t2.t38 t73.t2.t40))
% 54.31/54.53  (step t73.t2.t42 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule refl)
% 54.31/54.53  (step t73.t2.t43 (cl (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) tptp.identity)) :rule symm :premises (t73.t2.a34))
% 54.31/54.53  (step t73.t2.t44 (cl (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) :rule symm :premises (t73.t2.t43))
% 54.31/54.53  (step t73.t2.t45 (cl (= (tptp.inverse tptp.a) (tptp.inverse tptp.a))) :rule refl)
% 54.31/54.53  (step t73.t2.t46 (cl (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) :rule symm :premises (t73.t2.a33))
% 54.31/54.53  (step t73.t2.t47 (cl (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule symm :premises (t73.t2.t46))
% 54.31/54.53  (step t73.t2.t48 (cl (= (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule cong :premises (t73.t2.t45 t73.t2.t47))
% 54.31/54.53  (step t73.t2.t49 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule symm :premises (t73.t2.a32))
% 54.31/54.53  (step t73.t2.t50 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule symm :premises (t73.t2.t49))
% 54.31/54.53  (step t73.t2.t51 (cl (= tptp.identity (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule trans :premises (t73.t2.a2 t73.t2.t48 t73.t2.t50))
% 54.31/54.53  (step t73.t2.t52 (cl (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a))) :rule refl)
% 54.31/54.53  (step t73.t2.t53 (cl (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) :rule cong :premises (t73.t2.t51 t73.t2.t52))
% 54.31/54.53  (step t73.t2.t54 (cl (= (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))))) :rule symm :premises (t73.t2.a31))
% 54.31/54.53  (step t73.t2.t55 (cl (= (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))))) :rule symm :premises (t73.t2.a30))
% 54.31/54.53  (step t73.t2.t56 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule symm :premises (t73.t2.t55))
% 54.31/54.53  (step t73.t2.t57 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule refl)
% 54.31/54.53  (step t73.t2.t58 (cl (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) :rule cong :premises (t73.t2.t28 t73.t2.a22))
% 54.31/54.53  (step t73.t2.t59 (cl (= (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) :rule symm :premises (t73.t2.a27))
% 54.31/54.53  (step t73.t2.t60 (cl (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) :rule symm :premises (t73.t2.t59))
% 54.31/54.53  (step t73.t2.t61 (cl (= (tptp.multiply tptp.identity tptp.a) tptp.a)) :rule symm :premises (t73.t2.a4))
% 54.31/54.53  (step t73.t2.t62 (cl (= (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)) (tptp.greatest_lower_bound tptp.identity tptp.a))) :rule cong :premises (t73.t2.t39 t73.t2.t61))
% 54.31/54.53  (step t73.t2.t63 (cl (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) :rule trans :premises (t73.t2.t58 t73.t2.t60 t73.t2.t62))
% 54.31/54.53  (step t73.t2.t64 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)))) :rule cong :premises (t73.t2.t57 t73.t2.t63))
% 54.31/54.53  (step t73.t2.t65 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule symm :premises (t73.t2.t64))
% 54.31/54.53  (step t73.t2.t66 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule symm :premises (t73.t2.a28))
% 54.31/54.53  (step t73.t2.t67 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule trans :premises (t73.t2.t65 t73.t2.t66))
% 54.31/54.53  (step t73.t2.t68 (cl (= (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule refl)
% 54.31/54.53  (step t73.t2.t69 (cl (= (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule cong :premises (t73.t2.t67 t73.t2.t68))
% 54.31/54.53  (step t73.t2.t70 (cl (= (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule trans :premises (t73.t2.t22 t73.t2.t44 t73.t2.t53 t73.t2.t54 t73.t2.t56 t73.t2.t69))
% 54.31/54.53  (step t73.t2.t71 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule cong :premises (t73.t2.t42 t73.t2.t70))
% 54.31/54.53  (step t73.t2.t72 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule symm :premises (t73.t2.a29))
% 54.31/54.53  (step t73.t2.t73 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule symm :premises (t73.t2.t66))
% 54.31/54.53  (step t73.t2.t74 (cl (= (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) :rule symm :premises (t73.t2.a1))
% 54.31/54.53  (step t73.t2.t75 (cl (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) :rule refl)
% 54.31/54.53  (step t73.t2.t76 (cl (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule cong :premises (t73.t2.t74 t73.t2.t75))
% 54.31/54.53  (step t73.t2.t77 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule symm :premises (t73.t2.t76))
% 54.31/54.53  (step t73.t2.t78 (cl (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule symm :premises (t73.t2.a26))
% 54.31/54.53  (step t73.t2.t79 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule cong :premises (t73.t2.t22 t73.t2.t57))
% 54.31/54.53  (step t73.t2.t80 (cl (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule symm :premises (t73.t2.t79))
% 54.31/54.53  (step t73.t2.t81 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule trans :premises (t73.t2.t77 t73.t2.t78 t73.t2.t80))
% 54.31/54.53  (step t73.t2.t82 (cl (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule symm :premises (t73.t2.t78))
% 54.31/54.53  (step t73.t2.t83 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule symm :premises (t73.t2.a21))
% 54.31/54.53  (step t73.t2.t84 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) :rule symm :premises (t73.t2.t83))
% 54.31/54.53  (step t73.t2.t85 (cl (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.identity tptp.identity))) :rule cong :premises (t73.t2.t28 t73.t2.t22))
% 54.31/54.53  (step t73.t2.t86 (cl (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity)) :rule trans :premises (t73.t2.t85 t73.t2.t39))
% 54.31/54.53  (step t73.t2.t87 (cl (= tptp.identity (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule symm :premises (t73.t2.t86))
% 54.31/54.53  (step t73.t2.t88 (cl (= (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule trans :premises (t73.t2.t22 t73.t2.t87))
% 54.31/54.53  (step t73.t2.t89 (cl (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) :rule cong :premises (t73.t2.t74 t73.t2.t28))
% 54.31/54.53  (step t73.t2.t90 (cl (= (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity))) :rule symm :premises (t73.t2.t89))
% 54.31/54.53  (step t73.t2.t91 (cl (= (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) :rule trans :premises (t73.t2.t90 t73.t2.a20))
% 54.31/54.53  (step t73.t2.t92 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))))) :rule cong :premises (t73.t2.t88 t73.t2.t91))
% 54.31/54.53  (step t73.t2.t93 (cl (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity))) :rule symm :premises (t73.t2.a20))
% 54.31/54.53  (step t73.t2.t94 (cl (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a)))) :rule refl)
% 54.31/54.53  (step t73.t2.t95 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) :rule cong :premises (t73.t2.t94 t73.t2.a1))
% 54.31/54.53  (step t73.t2.t96 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)))) :rule symm :premises (t73.t2.a7))
% 54.31/54.53  (step t73.t2.t97 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule cong :premises (t73.t2.t94 t73.t2.a2))
% 54.31/54.53  (step t73.t2.t98 (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 (t73.t2.a6))
% 54.31/54.53  (step t73.t2.t99 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.identity)) :rule symm :premises (t73.t2.a5))
% 54.31/54.53  (step t73.t2.t100 (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 (t73.t2.t99 t73.t2.t17))
% 54.31/54.53  (step t73.t2.t101 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) tptp.a)) :rule trans :premises (t73.t2.t97 t73.t2.t98 t73.t2.t100 t73.t2.t61))
% 54.31/54.53  (step t73.t2.t102 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) :rule cong :premises (t73.t2.t101 t73.t2.t45))
% 54.31/54.53  (step t73.t2.t103 (cl (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a)))) :rule trans :premises (t73.t2.a5 t73.t2.t95 t73.t2.t96 t73.t2.t102))
% 54.31/54.53  (step t73.t2.t104 (cl (= (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule cong :premises (t73.t2.t45 t73.t2.t103))
% 54.31/54.53  (step t73.t2.t105 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)))) :rule symm :premises (t73.t2.a3))
% 54.31/54.53  (step t73.t2.t106 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) :rule cong :premises (t73.t2.t22 t73.t2.t45))
% 54.31/54.53  (step t73.t2.t107 (cl (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)) (tptp.inverse tptp.a))) :rule trans :premises (t73.t2.t93 t73.t2.t89 t73.t2.t104 t73.t2.t105 t73.t2.t106 t73.t2.t74))
% 54.31/54.53  (step t73.t2.t108 (cl (= (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) :rule cong :premises (t73.t2.t86 t73.t2.t107))
% 54.31/54.53  (step t73.t2.t109 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) :rule trans :premises (t73.t2.t79 t73.t2.t82 t73.t2.t76 t73.t2.t84 t73.t2.t92 t73.t2.t108 t73.t2.a19))
% 54.31/54.53  (step t73.t2.t110 (cl (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) :rule symm :premises (t73.t2.a19))
% 54.31/54.53  (step t73.t2.t111 (cl (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))))) :rule symm :premises (t73.t2.t108))
% 54.31/54.53  (step t73.t2.t112 (cl (= (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) :rule symm :premises (t73.t2.t92))
% 54.31/54.53  (step t73.t2.t113 (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 (t73.t2.t100))
% 54.31/54.53  (step t73.t2.t114 (cl (= (tptp.multiply tptp.identity tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) :rule cong :premises (t73.t2.a2 t73.t2.t28))
% 54.31/54.53  (step t73.t2.t115 (cl (= (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) :rule trans :premises (t73.t2.t22 t73.t2.a10 t73.t2.t114))
% 54.31/54.53  (step t73.t2.t116 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) :rule cong :premises (t73.t2.t94 t73.t2.t115))
% 54.31/54.53  (step t73.t2.t117 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity))) :rule symm :premises (t73.t2.a25))
% 54.31/54.53  (step t73.t2.t118 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.a)) :rule trans :premises (t73.t2.t98 t73.t2.t100 t73.t2.t61))
% 54.31/54.53  (step t73.t2.t119 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.identity tptp.a))) :rule trans :premises (t73.t2.t118 t73.t2.a4))
% 54.31/54.53  (step t73.t2.t120 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.multiply tptp.identity tptp.a) tptp.identity))) :rule cong :premises (t73.t2.t119 t73.t2.t28))
% 54.31/54.53  (step t73.t2.t121 (cl (= (tptp.multiply (tptp.multiply tptp.identity tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) :rule cong :premises (t73.t2.t61 t73.t2.t28))
% 54.31/54.53  (step t73.t2.t122 (cl (= tptp.a (tptp.multiply tptp.a tptp.identity))) :rule trans :premises (t73.t2.a4 t73.t2.t113 t73.t2.a6 t73.t2.t116 t73.t2.t117 t73.t2.t120 t73.t2.t121))
% 54.31/54.53  (step t73.t2.t123 (cl (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) :rule cong :premises (t73.t2.a10 t73.t2.t122))
% 54.31/54.53  (step t73.t2.t124 (cl (= (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity))) :rule symm :premises (t73.t2.a24))
% 54.31/54.53  (step t73.t2.t125 (cl (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) :rule symm :premises (t73.t2.a22))
% 54.31/54.53  (step t73.t2.t126 (cl (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) :rule cong :premises (t73.t2.t125 t73.t2.t28))
% 54.31/54.53  (step t73.t2.t127 (cl (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) :rule trans :premises (t73.t2.a22 t73.t2.t123 t73.t2.t124 t73.t2.t126))
% 54.31/54.53  (step t73.t2.t128 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) :rule cong :premises (t73.t2.t45 t73.t2.t127))
% 54.31/54.53  (step t73.t2.t129 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) :rule symm :premises (t73.t2.a23))
% 54.31/54.53  (step t73.t2.t130 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) :rule cong :premises (t73.t2.t84 t73.t2.t28))
% 54.31/54.53  (step t73.t2.t131 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule cong :premises (t73.t2.t45 t73.t2.t125))
% 54.31/54.53  (step t73.t2.t132 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)))) :rule symm :premises (t73.t2.t131))
% 54.31/54.53  (step t73.t2.t133 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) :rule trans :premises (t73.t2.t131 t73.t2.t84 t73.t2.t92 t73.t2.t108))
% 54.31/54.53  (step t73.t2.t134 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) :rule trans :premises (t73.t2.t83 t73.t2.t132 t73.t2.t133 t73.t2.a19))
% 54.31/54.53  (step t73.t2.t135 (cl (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) :rule cong :premises (t73.t2.t134 t73.t2.t28))
% 54.31/54.53  (step t73.t2.t136 (cl (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule cong :premises (t73.t2.t110 t73.t2.t103))
% 54.31/54.53  (step t73.t2.t137 (cl (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)))) :rule symm :premises (t73.t2.a18))
% 54.31/54.53  (step t73.t2.t138 (cl (= (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a))) :rule symm :premises (t73.t2.a17))
% 54.31/54.53  (step t73.t2.t139 (cl (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule symm :premises (t73.t2.t138))
% 54.31/54.53  (step t73.t2.t140 (cl (= (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.identity))) :rule trans :premises (t73.t2.t22 t73.t2.a16))
% 54.31/54.53  (step t73.t2.t141 (cl (= (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.identity tptp.identity)))) :rule cong :premises (t73.t2.t61 t73.t2.t140))
% 54.31/54.53  (step t73.t2.t142 (cl (= (tptp.greatest_lower_bound tptp.identity tptp.identity) tptp.identity)) :rule symm :premises (t73.t2.a16))
% 54.31/54.53  (step t73.t2.t143 (cl (= (tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.identity tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) :rule cong :premises (t73.t2.t17 t73.t2.t142))
% 54.31/54.53  (step t73.t2.t144 (cl (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) :rule trans :premises (t73.t2.t139 t73.t2.t141 t73.t2.t143))
% 54.31/54.53  (step t73.t2.t145 (cl (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)))) :rule cong :premises (t73.t2.t144 t73.t2.t45))
% 54.31/54.53  (step t73.t2.t146 (cl (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)))) :rule trans :premises (t73.t2.t110 t73.t2.t111 t73.t2.t112 t73.t2.t83 t73.t2.t128 t73.t2.t129 t73.t2.t130 t73.t2.t135 t73.t2.t136 t73.t2.t137 t73.t2.t145))
% 54.31/54.53  (step t73.t2.t147 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)))) :rule trans :premises (t73.t2.t81 t73.t2.t109 t73.t2.t146))
% 54.31/54.53  (step t73.t2.t148 (cl (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) :rule trans :premises (t73.t2.t123 t73.t2.t124 t73.t2.t126))
% 54.31/54.53  (step t73.t2.t149 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) :rule cong :premises (t73.t2.t147 t73.t2.t148))
% 54.31/54.53  (step t73.t2.t150 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule symm :premises (t73.t2.a15))
% 54.31/54.53  (step t73.t2.t151 (cl (= tptp.identity (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule trans :premises (t73.t2.a2 t73.t2.t18 t73.t2.t20 t73.t2.t35 t73.t2.t37 t73.t2.t41 t73.t2.t71 t73.t2.t72 t73.t2.t73 t73.t2.t64 t73.t2.t149 t73.t2.t150))
% 54.31/54.53  (step t73.t2.t152 (cl (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule cong :premises (t73.t2.t11 t73.t2.t151))
% 54.31/54.53  (step t73.t2.t153 (cl (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule symm :premises (t73.t2.a14))
% 54.31/54.53  (step t73.t2.t154 (cl (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) :rule symm :premises (t73.t2.a13))
% 54.31/54.53  (step t73.t2.t155 (cl (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) :rule refl)
% 54.31/54.53  (step t73.t2.t156 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule cong :premises (t73.t2.t154 t73.t2.t155))
% 54.31/54.53  (step t73.t2.t157 (cl (= (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) :rule symm :premises (t73.t2.a12))
% 54.31/54.53  (step t73.t2.t158 (cl (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) :rule trans :premises (t73.t2.t152 t73.t2.t153 t73.t2.t156 t73.t2.t157))
% 54.31/54.53  (step t73.t2.t159 (cl (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule cong :premises (t73.t2.t125 t73.t2.t11))
% 54.31/54.53  (step t73.t2.t160 (cl (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) :rule symm :premises (t73.t2.t62))
% 54.31/54.53  (step t73.t2.t161 (cl (= (tptp.multiply tptp.identity tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity))) :rule cong :premises (t73.t2.a44 t73.t2.t28))
% 54.31/54.53  (step t73.t2.t162 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity))) :rule symm :premises (t73.t2.a49))
% 54.31/54.54  (step t73.t2.t163 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) :rule symm :premises (t73.t2.t162))
% 54.31/54.54  (step t73.t2.t164 (cl (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) :rule trans :premises (t73.t2.a10 t73.t2.t161 t73.t2.t163))
% 54.31/54.54  (step t73.t2.t165 (cl (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)))) :rule cong :premises (t73.t2.t164 t73.t2.t52))
% 54.31/54.54  (step t73.t2.t166 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)))) :rule symm :premises (t73.t2.a48))
% 54.31/54.54  (step t73.t2.t167 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) :rule symm :premises (t73.t2.t166))
% 54.31/54.54  (step t73.t2.t168 (cl (= (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule refl)
% 54.31/54.54  (step t73.t2.t169 (cl (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) :rule symm :premises (t73.t2.a47))
% 54.31/54.54  (step t73.t2.t170 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) :rule symm :premises (t73.t2.t169))
% 54.31/54.54  (step t73.t2.t171 (cl (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) :rule trans :premises (t73.t2.t60 t73.t2.t62 t73.t2.t125))
% 54.31/54.54  (step t73.t2.t172 (cl (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule cong :premises (t73.t2.t11 t73.t2.t171))
% 54.31/54.54  (step t73.t2.t173 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) tptp.identity)) :rule trans :premises (t73.t2.t170 t73.t2.t172 t73.t2.t154))
% 54.31/54.54  (step t73.t2.t174 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity))) :rule cong :premises (t73.t2.t168 t73.t2.t173))
% 54.31/54.54  (step t73.t2.t175 (cl (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity))) :rule trans :premises (t73.t2.a22 t73.t2.t160 t73.t2.t59 t73.t2.t165 t73.t2.t167 t73.t2.t174))
% 54.31/54.54  (step t73.t2.t176 (cl (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule cong :premises (t73.t2.t175 t73.t2.t11))
% 54.31/54.54  (step t73.t2.t177 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule symm :premises (t73.t2.a46))
% 54.31/54.54  (step t73.t2.t178 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule symm :premises (t73.t2.t177))
% 54.31/54.54  (step t73.t2.t179 (cl (= (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule symm :premises (t73.t2.a45))
% 54.31/54.54  (step t73.t2.t180 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule cong :premises (t73.t2.t168 t73.t2.t179))
% 54.31/54.54  (step t73.t2.t181 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity)) :rule symm :premises (t73.t2.a44))
% 54.31/54.54  (step t73.t2.t182 (cl (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity)) :rule trans :premises (t73.t2.t159 t73.t2.t176 t73.t2.t178 t73.t2.t180 t73.t2.t181))
% 54.31/54.54  (step t73.t2.t183 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) :rule cong :premises (t73.t2.t158 t73.t2.t182))
% 54.31/54.54  (step t73.t2.t184 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) :rule symm :premises (t73.t2.a11))
% 54.31/54.54  (step t73.t2.t185 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) :rule symm :premises (t73.t2.t184))
% 54.31/54.54  (step t73.t2.t186 (cl (= (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) :rule refl)
% 54.31/54.54  (step t73.t2.t187 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule cong :premises (t73.t2.t186 t73.t2.t40))
% 54.31/54.54  (step t73.t2.t188 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) :rule cong :premises (t73.t2.t45 t73.t2.t22))
% 54.31/54.54  (step t73.t2.t189 (cl (= (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule symm :premises (t73.t2.t188))
% 54.31/54.54  (step t73.t2.t190 (cl (= (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) :rule symm :premises (t73.t2.a8))
% 54.31/54.54  (step t73.t2.t191 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) :rule cong :premises (t73.t2.t45 t73.t2.t190))
% 54.31/54.54  (step t73.t2.t192 (cl (= (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule symm :premises (t73.t2.t191))
% 54.31/54.54  (step t73.t2.t193 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule symm :premises (t73.t2.a9))
% 54.31/54.54  (step t73.t2.t194 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule trans :premises (t73.t2.t188 t73.t2.t192 t73.t2.t193))
% 54.31/54.54  (step t73.t2.t195 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule symm :premises (t73.t2.t193))
% 54.31/54.54  (step t73.t2.t196 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.inverse tptp.a))) :rule trans :premises (t73.t2.t195 t73.t2.t191 t73.t2.t104 t73.t2.t105 t73.t2.t106 t73.t2.t74))
% 54.31/54.54  (step t73.t2.t197 (cl (= (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) :rule trans :premises (t73.t2.t189 t73.t2.t194 t73.t2.t196))
% 54.31/54.54  (step t73.t2.t198 (cl (= (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound tptp.identity tptp.identity))) :rule trans :premises (t73.t2.t22 t73.t2.a0))
% 54.31/54.54  (step t73.t2.t199 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.identity tptp.identity)))) :rule cong :premises (t73.t2.t197 t73.t2.t198))
% 54.31/54.54  (step t73.t2.t200 (cl (= (tptp.least_upper_bound tptp.identity tptp.identity) tptp.identity)) :rule symm :premises (t73.t2.a0))
% 54.31/54.54  (step t73.t2.t201 (cl (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.identity tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) :rule cong :premises (t73.t2.t45 t73.t2.t200))
% 54.31/54.54  (step t73.t2.t202 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) :rule trans :premises (t73.t2.t183 t73.t2.t185 t73.t2.t187 t73.t2.t199 t73.t2.t201))
% 54.31/54.54  (step t73.t2.t203 (cl (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule cong :premises (t73.t2.t173 t73.t2.t11))
% 54.31/54.54  (step t73.t2.t204 (cl (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule trans :premises (t73.t2.t203 t73.t2.t179))
% 54.31/54.54  (step t73.t2.t205 (cl (= (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule cong :premises (t73.t2.t202 t73.t2.t204))
% 54.31/54.54  (step t73.t2.t206 (cl (= (= (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) false) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule equiv_simplify)
% 54.31/54.54  (step t73.t2.t207 (cl (= (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) false) (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule equiv2 :premises (t73.t2.t206))
% 54.31/54.54  (step t73.t2.t208 (cl (not (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule not_not)
% 54.31/54.54  (step t73.t2.t209 (cl (= (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) false) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule resolution :premises (t73.t2.t207 t73.t2.t208))
% 54.31/54.54  (step t73.t2.t210 (cl (= (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) false)) :rule resolution :premises (t73.t2.t209 t73.t2.a50))
% 54.31/54.54  (step t73.t2.t211 (cl (= (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) false)) :rule trans :premises (t73.t2.t205 t73.t2.t210))
% 54.31/54.54  (step t73.t2.t212 (cl (= (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) false)) :rule resolution :premises (t73.t2.t3 t73.t2.t10 t73.t2.t211))
% 54.31/54.54  (step t73.t2.t213 (cl (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) :rule resolution :premises (t73.t2.t2 t73.t2.t212))
% 54.31/54.54  (step t73.t2 (cl (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse 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.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) :rule subproof :discharge (t73.t2.a0 t73.t2.a1 t73.t2.a2 t73.t2.a3 t73.t2.a4 t73.t2.a5 t73.t2.a6 t73.t2.a7 t73.t2.a8 t73.t2.a9 t73.t2.a10 t73.t2.a11 t73.t2.a12 t73.t2.a13 t73.t2.a14 t73.t2.a15 t73.t2.a16 t73.t2.a17 t73.t2.a18 t73.t2.a19 t73.t2.a20 t73.t2.a21 t73.t2.a22 t73.t2.a23 t73.t2.a24 t73.t2.a25 t73.t2.a26 t73.t2.a27 t73.t2.a28 t73.t2.a29 t73.t2.a30 t73.t2.a31 t73.t2.a32 t73.t2.a33 t73.t2.a34 t73.t2.a35 t73.t2.a36 t73.t2.a37 t73.t2.a38 t73.t2.a39 t73.t2.a40 t73.t2.a41 t73.t2.a42 t73.t2.a43 t73.t2.a44 t73.t2.a45 t73.t2.a46 t73.t2.a47 t73.t2.a48 t73.t2.a49 t73.t2.a50))
% 54.31/54.54  (step t73.t3 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) :rule and_pos)
% 54.31/54.54  (step t73.t4 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) :rule and_pos)
% 54.31/54.54  (step t73.t5 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule and_pos)
% 54.31/54.54  (step t73.t6 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule and_pos)
% 54.31/54.54  (step t73.t7 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) :rule and_pos)
% 54.31/54.54  (step t73.t8 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (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)
% 54.31/54.54  (step t73.t9 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (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)
% 54.31/54.54  (step t73.t10 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) :rule and_pos)
% 54.31/54.54  (step t73.t11 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule and_pos)
% 54.31/54.54  (step t73.t12 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule and_pos)
% 54.31/54.54  (step t73.t13 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) :rule and_pos)
% 54.31/54.54  (step t73.t14 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) :rule and_pos)
% 54.31/54.54  (step t73.t15 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule and_pos)
% 54.31/54.54  (step t73.t16 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule and_pos)
% 54.31/54.54  (step t73.t17 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule and_pos)
% 54.31/54.54  (step t73.t18 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) :rule and_pos)
% 54.31/54.54  (step t73.t19 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) :rule and_pos)
% 54.31/54.54  (step t73.t20 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule and_pos)
% 54.31/54.54  (step t73.t21 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule and_pos)
% 54.31/54.54  (step t73.t22 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) :rule and_pos)
% 54.31/54.54  (step t73.t23 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) :rule and_pos)
% 54.31/54.54  (step t73.t24 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) :rule and_pos)
% 54.31/54.54  (step t73.t25 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (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)
% 54.31/54.54  (step t73.t26 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) :rule and_pos)
% 54.31/54.54  (step t73.t27 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) :rule and_pos)
% 54.31/54.54  (step t73.t28 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) :rule and_pos)
% 54.31/54.54  (step t73.t29 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule and_pos)
% 54.31/54.54  (step t73.t30 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) :rule and_pos)
% 54.31/54.54  (step t73.t31 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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)
% 54.31/54.54  (step t73.t32 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule and_pos)
% 54.31/54.54  (step t73.t33 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule and_pos)
% 54.31/54.54  (step t73.t34 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) :rule and_pos)
% 54.31/54.54  (step t73.t35 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule and_pos)
% 54.31/54.54  (step t73.t36 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (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 and_pos)
% 54.31/54.54  (step t73.t37 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (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)
% 54.31/54.54  (step t73.t38 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) :rule and_pos)
% 54.31/54.54  (step t73.t39 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) :rule and_pos)
% 54.31/54.54  (step t73.t40 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) :rule and_pos)
% 54.31/54.54  (step t73.t41 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) :rule and_pos)
% 54.31/54.54  (step t73.t42 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) :rule and_pos)
% 54.31/54.54  (step t73.t43 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) :rule and_pos)
% 54.31/54.54  (step t73.t44 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule and_pos)
% 54.31/54.54  (step t73.t45 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) :rule and_pos)
% 54.31/54.54  (step t73.t46 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule and_pos)
% 54.31/54.54  (step t73.t47 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule and_pos)
% 54.31/54.54  (step t73.t48 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule and_pos)
% 54.31/54.54  (step t73.t49 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule and_pos)
% 54.31/54.54  (step t73.t50 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) :rule and_pos)
% 54.31/54.54  (step t73.t51 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) :rule and_pos)
% 54.31/54.54  (step t73.t52 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) :rule and_pos)
% 54.31/54.54  (step t73.t53 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule and_pos)
% 54.31/54.54  (step t73.t54 (cl (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) :rule resolution :premises (t73.t2 t73.t3 t73.t4 t73.t5 t73.t6 t73.t7 t73.t8 t73.t9 t73.t10 t73.t11 t73.t12 t73.t13 t73.t14 t73.t15 t73.t16 t73.t17 t73.t18 t73.t19 t73.t20 t73.t21 t73.t22 t73.t23 t73.t24 t73.t25 t73.t26 t73.t27 t73.t28 t73.t29 t73.t30 t73.t31 t73.t32 t73.t33 t73.t34 t73.t35 t73.t36 t73.t37 t73.t38 t73.t39 t73.t40 t73.t41 t73.t42 t73.t43 t73.t44 t73.t45 t73.t46 t73.t47 t73.t48 t73.t49 t73.t50 t73.t51 t73.t52 t73.t53))
% 54.31/54.54  (step t73.t55 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) :rule reordering :premises (t73.t54))
% 54.31/54.55  (step t73.t56 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) :rule contraction :premises (t73.t55))
% 54.31/54.55  (step t73.t57 (cl (=> (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) :rule resolution :premises (t73.t1 t73.t56))
% 54.31/54.55  (step t73.t58 (cl (=> (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))))) :rule implies_neg2)
% 54.31/54.55  (step t73.t59 (cl (=> (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (=> (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))))) :rule resolution :premises (t73.t57 t73.t58))
% 54.31/54.55  (step t73.t60 (cl (=> (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))))) :rule contraction :premises (t73.t59))
% 54.31/54.55  (step t73.t61 (cl (not (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) :rule implies :premises (t73.t60))
% 54.31/54.55  (step t73.t62 (cl (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse 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.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule and_neg)
% 54.31/54.55  (step t73.t63 (cl (and (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse 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.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse 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.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule resolution :premises (t73.t62 t73.a9 t73.a27 t73.a1 t73.a42 t73.a15 t73.a16 t73.a19 t73.a34 t73.a28 t73.a35 t73.a7 t73.a39 t73.a32 t73.a2 t73.a47 t73.a37 t73.a10 t73.a23 t73.a43 t73.a8 t73.a33 t73.a25 t73.a3 t73.a44 t73.a26 t73.a30 t73.a29 t73.a17 t73.a31 t73.a46 t73.a38 t73.a24 t73.a14 t73.a5 t73.a12 t73.a36 t73.a45 t73.a22 t73.a4 t73.a18 t73.a13 t73.a21 t73.a11 t73.a6 t73.a41 t73.a40 t73.a49 t73.a20 t73.a50 t73.a48 t73.a0))
% 54.31/54.55  (step t73.t64 (cl (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) :rule resolution :premises (t73.t61 t73.t63))
% 54.31/54.55  (step t73 (cl (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) :rule subproof :discharge (t73.a0 t73.a1 t73.a2 t73.a3 t73.a4 t73.a5 t73.a6 t73.a7 t73.a8 t73.a9 t73.a10 t73.a11 t73.a12 t73.a13 t73.a14 t73.a15 t73.a16 t73.a17 t73.a18 t73.a19 t73.a20 t73.a21 t73.a22 t73.a23 t73.a24 t73.a25 t73.a26 t73.a27 t73.a28 t73.a29 t73.a30 t73.a31 t73.a32 t73.a33 t73.a34 t73.a35 t73.a36 t73.a37 t73.a38 t73.a39 t73.a40 t73.a41 t73.a42 t73.a43 t73.a44 t73.a45 t73.a46 t73.a47 t73.a48 t73.a49 t73.a50))
% 54.31/54.55  (step t74 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule and_pos)
% 54.31/54.55  (step t75 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule and_pos)
% 54.31/54.55  (step t76 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule and_pos)
% 54.31/54.55  (step t77 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) :rule and_pos)
% 54.31/54.55  (step t78 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) :rule and_pos)
% 54.31/54.55  (step t79 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule and_pos)
% 54.31/54.55  (step t80 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule and_pos)
% 54.31/54.55  (step t81 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) :rule and_pos)
% 54.31/54.55  (step t82 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) :rule and_pos)
% 54.31/54.55  (step t83 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) :rule and_pos)
% 54.31/54.55  (step t84 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) :rule and_pos)
% 54.31/54.55  (step t85 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) :rule and_pos)
% 54.31/54.55  (step t86 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) 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 and_pos)
% 54.31/54.55  (step t87 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) :rule and_pos)
% 54.31/54.55  (step t88 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule and_pos)
% 54.31/54.55  (step t89 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) :rule and_pos)
% 54.31/54.55  (step t90 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule and_pos)
% 54.31/54.55  (step t91 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) :rule and_pos)
% 54.31/54.55  (step t92 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) :rule and_pos)
% 54.31/54.55  (step t93 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity 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)
% 54.31/54.55  (step t94 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) :rule and_pos)
% 54.31/54.55  (step t95 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule and_pos)
% 54.31/54.55  (step t96 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) :rule and_pos)
% 54.31/54.55  (step t97 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule and_pos)
% 54.31/54.55  (step t98 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) :rule and_pos)
% 54.31/54.55  (step t99 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) :rule and_pos)
% 54.31/54.55  (step t100 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) :rule and_pos)
% 54.31/54.55  (step t101 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) :rule and_pos)
% 54.31/54.55  (step t102 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule and_pos)
% 54.31/54.55  (step t103 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule and_pos)
% 54.31/54.55  (step t104 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) :rule and_pos)
% 54.31/54.55  (step t105 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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)
% 54.31/54.55  (step t106 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule and_pos)
% 54.31/54.55  (step t107 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) :rule and_pos)
% 54.31/54.55  (step t108 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) :rule and_pos)
% 54.31/54.55  (step t109 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule and_pos)
% 54.31/54.55  (step t110 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) :rule and_pos)
% 54.31/54.55  (step t111 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) :rule and_pos)
% 54.31/54.55  (step t112 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule and_pos)
% 54.31/54.55  (step t113 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) :rule and_pos)
% 54.31/54.55  (step t114 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule and_pos)
% 54.31/54.55  (step t115 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule and_pos)
% 54.31/54.55  (step t116 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule and_pos)
% 54.31/54.55  (step t117 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule and_pos)
% 54.31/54.55  (step t118 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) :rule and_pos)
% 54.31/54.55  (step t119 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) :rule and_pos)
% 54.31/54.55  (step t120 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule and_pos)
% 54.31/54.55  (step t121 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule and_pos)
% 54.31/54.55  (step t122 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) :rule and_pos)
% 54.31/54.55  (step t123 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule and_pos)
% 54.31/54.55  (step t124 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) :rule and_pos)
% 54.31/54.55  (step t125 (cl (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))))) :rule resolution :premises (t73 t74 t75 t76 t77 t78 t79 t80 t81 t82 t83 t84 t85 t86 t87 t88 t89 t90 t91 t92 t93 t94 t95 t96 t97 t98 t99 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))
% 54.31/54.56  (step t126 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) :rule reordering :premises (t125))
% 54.31/54.56  (step t127 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) :rule contraction :premises (t126))
% 54.31/54.56  (step t128 (cl (=> (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) :rule resolution :premises (t72 t127))
% 54.31/54.56  (step t129 (cl (=> (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))))) :rule implies_neg2)
% 54.31/54.56  (step t130 (cl (=> (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (=> (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))))) :rule resolution :premises (t128 t129))
% 54.31/54.56  (step t131 (cl (=> (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))))) :rule contraction :premises (t130))
% 54.31/54.56  (step t132 (cl (not (and (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) :rule implies :premises (t131))
% 54.31/54.56  (step t133 (cl (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) :rule resolution :premises (t71 t132))
% 54.31/54.56  (step t134 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) :rule or_neg)
% 54.31/54.56  (step t135 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule or_neg)
% 54.31/54.56  (step t136 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule or_neg)
% 54.31/54.56  (step t137 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) :rule or_neg)
% 54.31/54.56  (step t138 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))))) :rule or_neg)
% 54.31/54.56  (step t139 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule or_neg)
% 54.31/54.56  (step t140 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))))) :rule or_neg)
% 54.31/54.56  (step t141 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))))) :rule or_neg)
% 54.31/54.56  (step t142 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))))) :rule or_neg)
% 54.31/54.56  (step t143 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))))) :rule or_neg)
% 54.31/54.56  (step t144 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))))) :rule or_neg)
% 54.31/54.56  (step t145 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))))) :rule or_neg)
% 54.31/54.56  (step t146 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))))) :rule or_neg)
% 54.31/54.56  (step t147 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))))) :rule or_neg)
% 54.31/54.56  (step t148 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))))) :rule or_neg)
% 54.31/54.56  (step t149 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= tptp.a (tptp.multiply tptp.identity tptp.a))))) :rule or_neg)
% 54.31/54.56  (step t150 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) :rule or_neg)
% 54.31/54.56  (step t151 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))))) :rule or_neg)
% 54.31/54.56  (step t152 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))))) :rule or_neg)
% 54.31/54.56  (step t153 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (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)
% 54.31/54.56  (step t154 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))))) :rule or_neg)
% 54.31/54.56  (step t155 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule or_neg)
% 54.31/54.56  (step t156 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))))) :rule or_neg)
% 54.31/54.56  (step t157 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule or_neg)
% 54.31/54.56  (step t158 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) :rule or_neg)
% 54.31/54.56  (step t159 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))))) :rule or_neg)
% 54.31/54.56  (step t160 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))))) :rule or_neg)
% 54.31/54.56  (step t161 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))))) :rule or_neg)
% 54.31/54.56  (step t162 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))))) :rule or_neg)
% 54.31/54.56  (step t163 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule or_neg)
% 54.31/54.56  (step t164 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))))) :rule or_neg)
% 54.31/54.56  (step t165 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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)
% 54.31/54.56  (step t166 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))))) :rule or_neg)
% 54.31/54.56  (step t167 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))))) :rule or_neg)
% 54.31/54.56  (step t168 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))))) :rule or_neg)
% 54.31/54.56  (step t169 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))))) :rule or_neg)
% 54.31/54.56  (step t170 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))))) :rule or_neg)
% 54.31/54.56  (step t171 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))))) :rule or_neg)
% 54.31/54.56  (step t172 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule or_neg)
% 54.31/54.56  (step t173 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))))) :rule or_neg)
% 54.31/54.56  (step t174 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) :rule or_neg)
% 54.31/54.56  (step t175 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) :rule or_neg)
% 54.31/54.56  (step t176 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))))) :rule or_neg)
% 54.31/54.56  (step t177 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))))) :rule or_neg)
% 54.31/54.56  (step t178 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))))) :rule or_neg)
% 54.31/54.56  (step t179 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))))) :rule or_neg)
% 54.31/54.56  (step t180 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))))) :rule or_neg)
% 54.31/54.56  (step t181 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))))) :rule or_neg)
% 54.31/54.56  (step t182 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))))) :rule or_neg)
% 54.31/54.56  (step t183 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))))) :rule or_neg)
% 54.31/54.56  (step t184 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))))) :rule or_neg)
% 54.31/54.56  (step t185 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (not (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))))) :rule or_neg)
% 54.31/54.56  (step t186 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))))) :rule resolution :premises (t133 t134 t135 t136 t137 t138 t139 t140 t141 t142 t143 t144 t145 t146 t147 t148 t149 t150 t151 t152 t153 t154 t155 t156 t157 t158 t159 t160 t161 t162 t163 t164 t165 t166 t167 t168 t169 t170 t171 t172 t173 t174 t175 t176 t177 t178 t179 t180 t181 t182 t183 t184 t185))
% 54.31/54.57  (step t187 (cl (or (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))))) :rule contraction :premises (t186))
% 54.31/54.57  (step t188 (cl (or (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))))) :rule resolution :premises (t8 t70 t187))
% 54.31/54.57  (step t189 (cl (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse 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.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) :rule or :premises (t188))
% 54.31/54.57  (step t190 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) :rule implies_neg1)
% 54.31/54.57  (anchor :step t191)
% 54.31/54.57  (assume t191.a0 (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))))
% 54.31/54.57  (step t191.t1 (cl (or (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule forall_inst :args ((:= X tptp.a)))
% 54.31/54.57  (step t191.t2 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule or :premises (t191.t1))
% 54.31/54.57  (step t191.t3 (cl (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule resolution :premises (t191.t2 t191.a0))
% 54.31/54.57  (step t191 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule subproof :discharge (t191.a0))
% 54.31/54.57  (step t192 (cl (=> (forall ((X $$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 (t190 t191))
% 54.31/54.57  (step t193 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule implies_neg2)
% 54.31/54.57  (step t194 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule resolution :premises (t192 t193))
% 54.31/54.57  (step t195 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule contraction :premises (t194))
% 54.31/54.57  (step t196 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule implies :premises (t195))
% 54.31/54.57  (step t197 (cl (not (= (forall ((X $$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 $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) :rule equiv_pos2)
% 54.31/54.57  (anchor :step t198 :args ((X $$unsorted) (:= X X)))
% 54.31/54.57  (step t198.t1 (cl (= X X)) :rule refl)
% 54.31/54.57  (step t198.t2 (cl (= (= (tptp.multiply (tptp.inverse X) X) tptp.identity) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) :rule all_simplify)
% 54.31/54.57  (step t198 (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)
% 54.31/54.57  (step t199 (cl (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) :rule resolution :premises (t197 t198 a1))
% 54.31/54.57  (step t200 (cl (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule resolution :premises (t196 t199))
% 54.31/54.57  (step t201 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) :rule implies_neg1)
% 54.31/54.57  (anchor :step t202)
% 54.31/54.57  (assume t202.a0 (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))))
% 54.31/54.57  (step t202.t1 (cl (or (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule forall_inst :args ((:= X (tptp.greatest_lower_bound tptp.a tptp.identity))))
% 54.31/54.57  (step t202.t2 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule or :premises (t202.t1))
% 54.31/54.57  (step t202.t3 (cl (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule resolution :premises (t202.t2 t202.a0))
% 54.31/54.57  (step t202 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule subproof :discharge (t202.a0))
% 54.31/54.57  (step t203 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule resolution :premises (t201 t202))
% 54.31/54.57  (step t204 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule implies_neg2)
% 54.31/54.57  (step t205 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule resolution :premises (t203 t204))
% 54.31/54.57  (step t206 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule contraction :premises (t205))
% 54.31/54.57  (step t207 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule implies :premises (t206))
% 54.31/54.57  (step t208 (cl (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule resolution :premises (t207 t199))
% 54.31/54.57  (step t209 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) :rule implies_neg1)
% 54.31/54.57  (anchor :step t210)
% 54.31/54.57  (assume t210.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))))
% 54.31/54.57  (step t210.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) :rule forall_inst :args ((:= X tptp.a) (:= Y tptp.identity)))
% 54.31/54.57  (step t210.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) :rule or :premises (t210.t1))
% 54.31/54.57  (step t210.t3 (cl (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) :rule resolution :premises (t210.t2 t210.a0))
% 54.31/54.57  (step t210 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) :rule subproof :discharge (t210.a0))
% 54.31/54.57  (step t211 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) :rule resolution :premises (t209 t210))
% 54.31/54.57  (step t212 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) :rule implies_neg2)
% 54.31/54.57  (step t213 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) :rule resolution :premises (t211 t212))
% 54.31/54.57  (step t214 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))) :rule contraction :premises (t213))
% 54.31/54.57  (step t215 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) :rule implies :premises (t214))
% 54.31/54.57  (step t216 (cl (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) :rule resolution :premises (t215 a3))
% 54.31/54.57  (step t217 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) :rule implies_neg1)
% 54.31/54.57  (anchor :step t218)
% 54.31/54.57  (assume t218.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))))
% 54.31/54.57  (step t218.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.a)) (:= Y tptp.identity)))
% 54.31/54.57  (step t218.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) :rule or :premises (t218.t1))
% 54.31/54.57  (step t218.t3 (cl (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) :rule resolution :premises (t218.t2 t218.a0))
% 54.31/54.57  (step t218 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) :rule subproof :discharge (t218.a0))
% 54.31/54.57  (step t219 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) :rule resolution :premises (t217 t218))
% 54.31/54.57  (step t220 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) :rule implies_neg2)
% 54.31/54.57  (step t221 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) :rule resolution :premises (t219 t220))
% 54.31/54.57  (step t222 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) :rule contraction :premises (t221))
% 54.31/54.57  (step t223 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) :rule implies :premises (t222))
% 54.31/54.57  (step t224 (cl (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) :rule resolution :premises (t223 a4))
% 54.31/54.57  (step t225 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) :rule implies_neg1)
% 54.31/54.57  (anchor :step t226)
% 54.31/54.57  (assume t226.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))))
% 54.31/54.57  (step t226.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule forall_inst :args ((:= X tptp.a) (:= Y tptp.identity)))
% 54.31/54.57  (step t226.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule or :premises (t226.t1))
% 54.31/54.57  (step t226.t3 (cl (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule resolution :premises (t226.t2 t226.a0))
% 54.31/54.57  (step t226 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule subproof :discharge (t226.a0))
% 54.31/54.57  (step t227 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule resolution :premises (t225 t226))
% 54.31/54.57  (step t228 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule implies_neg2)
% 54.31/54.57  (step t229 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule resolution :premises (t227 t228))
% 54.31/54.57  (step t230 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule contraction :premises (t229))
% 54.31/54.57  (step t231 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule implies :premises (t230))
% 54.31/54.57  (step t232 (cl (not (= (forall ((X $$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 $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) :rule equiv_pos2)
% 54.31/54.57  (anchor :step t233 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y)))
% 54.31/54.57  (step t233.t1 (cl (= X X)) :rule refl)
% 54.31/54.57  (step t233.t2 (cl (= Y Y)) :rule refl)
% 54.31/54.57  (step t233.t3 (cl (= (= (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)) X) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) :rule all_simplify)
% 54.31/54.57  (step t233 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)) X)) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))))) :rule bind)
% 54.31/54.57  (step t234 (cl (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) :rule resolution :premises (t232 t233 a9))
% 54.31/54.57  (step t235 (cl (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule resolution :premises (t231 t234))
% 54.31/54.57  (step t236 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) :rule implies_neg1)
% 54.31/54.57  (anchor :step t237)
% 54.31/54.57  (assume t237.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))))
% 54.31/54.57  (step t237.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.a)) (:= Y tptp.identity)))
% 54.31/54.57  (step t237.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule or :premises (t237.t1))
% 54.31/54.57  (step t237.t3 (cl (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule resolution :premises (t237.t2 t237.a0))
% 54.31/54.57  (step t237 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule subproof :discharge (t237.a0))
% 54.31/54.57  (step t238 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule resolution :premises (t236 t237))
% 54.31/54.57  (step t239 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule implies_neg2)
% 54.31/54.57  (step t240 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule resolution :premises (t238 t239))
% 54.31/54.57  (step t241 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule contraction :premises (t240))
% 54.31/54.57  (step t242 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule implies :premises (t241))
% 54.31/54.57  (step t243 (cl (not (= (forall ((X $$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 $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) :rule equiv_pos2)
% 54.31/54.57  (anchor :step t244 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y)))
% 54.31/54.57  (step t244.t1 (cl (= X X)) :rule refl)
% 54.31/54.57  (step t244.t2 (cl (= Y Y)) :rule refl)
% 54.31/54.57  (step t244.t3 (cl (= (= (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)) X) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) :rule all_simplify)
% 54.31/54.57  (step t244 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)) X)) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))))) :rule bind)
% 54.31/54.57  (step t245 (cl (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) :rule resolution :premises (t243 t244 a10))
% 54.31/54.57  (step t246 (cl (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule resolution :premises (t242 t245))
% 54.31/54.57  (step t247 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) :rule implies_neg1)
% 54.31/54.57  (anchor :step t248)
% 54.31/54.57  (assume t248.a0 (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))))
% 54.31/54.57  (step t248.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)))) :rule forall_inst :args ((:= X tptp.identity)))
% 54.31/54.57  (step t248.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) :rule or :premises (t248.t1))
% 54.31/54.57  (step t248.t3 (cl (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) :rule resolution :premises (t248.t2 t248.a0))
% 54.31/54.57  (step t248 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) :rule subproof :discharge (t248.a0))
% 54.31/54.57  (step t249 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) :rule resolution :premises (t247 t248))
% 54.31/54.57  (step t250 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (not (= tptp.identity (tptp.multiply tptp.identity tptp.identity)))) :rule implies_neg2)
% 54.31/54.57  (step t251 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)))) :rule resolution :premises (t249 t250))
% 54.31/54.57  (step t252 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity)))) :rule contraction :premises (t251))
% 54.31/54.57  (step t253 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) :rule implies :premises (t252))
% 54.31/54.57  (step t254 (cl (not (= (forall ((X $$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 $$unsorted)) (= X (tptp.multiply tptp.identity X)))) :rule equiv_pos2)
% 54.31/54.57  (anchor :step t255 :args ((X $$unsorted) (:= X X)))
% 54.31/54.57  (step t255.t1 (cl (= X X)) :rule refl)
% 54.31/54.57  (step t255.t2 (cl (= (= (tptp.multiply tptp.identity X) X) (= X (tptp.multiply tptp.identity X)))) :rule all_simplify)
% 54.31/54.57  (step t255 (cl (= (forall ((X $$unsorted)) (= (tptp.multiply tptp.identity X) X)) (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))))) :rule bind)
% 54.31/54.57  (step t256 (cl (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) :rule resolution :premises (t254 t255 a0))
% 54.31/54.57  (step t257 (cl (= tptp.identity (tptp.multiply tptp.identity tptp.identity))) :rule resolution :premises (t253 t256))
% 54.31/54.57  (step t258 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) :rule implies_neg1)
% 54.31/54.57  (anchor :step t259)
% 54.31/54.57  (assume t259.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))))
% 54.31/54.57  (step t259.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)))) :rule forall_inst :args ((:= X tptp.identity) (:= Y (tptp.inverse tptp.a))))
% 54.31/54.57  (step t259.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) :rule or :premises (t259.t1))
% 54.31/54.57  (step t259.t3 (cl (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) :rule resolution :premises (t259.t2 t259.a0))
% 54.31/54.57  (step t259 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) :rule subproof :discharge (t259.a0))
% 54.31/54.57  (step t260 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) :rule resolution :premises (t258 t259))
% 54.31/54.57  (step t261 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)))) :rule implies_neg2)
% 54.31/54.57  (step t262 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)))) :rule resolution :premises (t260 t261))
% 54.31/54.57  (step t263 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity)))) :rule contraction :premises (t262))
% 54.31/54.57  (step t264 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) :rule implies :premises (t263))
% 54.31/54.57  (step t265 (cl (= (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) :rule resolution :premises (t264 a3))
% 54.31/54.57  (step t266 (cl (=> (forall ((X $$unsorted)) (= X (tptp.least_upper_bound X X))) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (forall ((X $$unsorted)) (= X (tptp.least_upper_bound X X)))) :rule implies_neg1)
% 54.31/54.57  (anchor :step t267)
% 54.31/54.57  (assume t267.a0 (forall ((X $$unsorted)) (= X (tptp.least_upper_bound X X))))
% 54.31/54.57  (step t267.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.least_upper_bound X X)))) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)))) :rule forall_inst :args ((:= X tptp.identity)))
% 54.31/54.57  (step t267.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.least_upper_bound X X)))) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) :rule or :premises (t267.t1))
% 54.31/54.57  (step t267.t3 (cl (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) :rule resolution :premises (t267.t2 t267.a0))
% 54.31/54.57  (step t267 (cl (not (forall ((X $$unsorted)) (= X (tptp.least_upper_bound X X)))) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) :rule subproof :discharge (t267.a0))
% 54.31/54.57  (step t268 (cl (=> (forall ((X $$unsorted)) (= X (tptp.least_upper_bound X X))) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) :rule resolution :premises (t266 t267))
% 54.31/54.57  (step t269 (cl (=> (forall ((X $$unsorted)) (= X (tptp.least_upper_bound X X))) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)))) :rule implies_neg2)
% 54.31/54.57  (step t270 (cl (=> (forall ((X $$unsorted)) (= X (tptp.least_upper_bound X X))) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) (=> (forall ((X $$unsorted)) (= X (tptp.least_upper_bound X X))) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)))) :rule resolution :premises (t268 t269))
% 54.31/54.57  (step t271 (cl (=> (forall ((X $$unsorted)) (= X (tptp.least_upper_bound X X))) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity)))) :rule contraction :premises (t270))
% 54.31/54.57  (step t272 (cl (not (forall ((X $$unsorted)) (= X (tptp.least_upper_bound X X)))) (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) :rule implies :premises (t271))
% 54.31/54.57  (step t273 (cl (not (= (forall ((X $$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 $$unsorted)) (= X (tptp.least_upper_bound X X)))) :rule equiv_pos2)
% 54.31/54.57  (anchor :step t274 :args ((X $$unsorted) (:= X X)))
% 54.31/54.57  (step t274.t1 (cl (= X X)) :rule refl)
% 54.31/54.57  (step t274.t2 (cl (= (= (tptp.least_upper_bound X X) X) (= X (tptp.least_upper_bound X X)))) :rule all_simplify)
% 54.31/54.57  (step t274 (cl (= (forall ((X $$unsorted)) (= (tptp.least_upper_bound X X) X)) (forall ((X $$unsorted)) (= X (tptp.least_upper_bound X X))))) :rule bind)
% 54.31/54.57  (step t275 (cl (forall ((X $$unsorted)) (= X (tptp.least_upper_bound X X)))) :rule resolution :premises (t273 t274 a7))
% 54.31/54.57  (step t276 (cl (= tptp.identity (tptp.least_upper_bound tptp.identity tptp.identity))) :rule resolution :premises (t272 t275))
% 54.31/54.57  (step t277 (cl (=> (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X)))) :rule implies_neg1)
% 54.31/54.57  (anchor :step t278)
% 54.31/54.57  (assume t278.a0 (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X))))
% 54.31/54.57  (step t278.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)))) :rule forall_inst :args ((:= X tptp.identity)))
% 54.31/54.57  (step t278.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) :rule or :premises (t278.t1))
% 54.31/54.57  (step t278.t3 (cl (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) :rule resolution :premises (t278.t2 t278.a0))
% 54.31/54.57  (step t278 (cl (not (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) :rule subproof :discharge (t278.a0))
% 54.31/54.57  (step t279 (cl (=> (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) :rule resolution :premises (t277 t278))
% 54.31/54.57  (step t280 (cl (=> (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)))) :rule implies_neg2)
% 54.31/54.57  (step t281 (cl (=> (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) (=> (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)))) :rule resolution :premises (t279 t280))
% 54.31/54.57  (step t282 (cl (=> (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity)))) :rule contraction :premises (t281))
% 54.31/54.57  (step t283 (cl (not (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) :rule implies :premises (t282))
% 54.31/54.57  (step t284 (cl (not (= (forall ((X $$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 $$unsorted)) (= X (tptp.greatest_lower_bound X X)))) :rule equiv_pos2)
% 54.31/54.57  (anchor :step t285 :args ((X $$unsorted) (:= X X)))
% 54.31/54.57  (step t285.t1 (cl (= X X)) :rule refl)
% 54.31/54.57  (step t285.t2 (cl (= (= (tptp.greatest_lower_bound X X) X) (= X (tptp.greatest_lower_bound X X)))) :rule all_simplify)
% 54.31/54.57  (step t285 (cl (= (forall ((X $$unsorted)) (= (tptp.greatest_lower_bound X X) X)) (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X))))) :rule bind)
% 54.31/54.57  (step t286 (cl (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X)))) :rule resolution :premises (t284 t285 a8))
% 54.31/54.57  (step t287 (cl (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.identity))) :rule resolution :premises (t283 t286))
% 54.31/54.57  (step t288 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) :rule implies_neg1)
% 54.31/54.57  (anchor :step t289)
% 54.31/54.57  (assume t289.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))))
% 54.31/54.57  (step t289.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.a)) (:= Y (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))
% 54.31/54.57  (step t289.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) :rule or :premises (t289.t1))
% 54.31/54.57  (step t289.t3 (cl (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) :rule resolution :premises (t289.t2 t289.a0))
% 54.31/54.57  (step t289 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) :rule subproof :discharge (t289.a0))
% 54.31/54.57  (step t290 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) :rule resolution :premises (t288 t289))
% 54.31/54.57  (step t291 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))))) :rule implies_neg2)
% 54.31/54.57  (step t292 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))))) :rule resolution :premises (t290 t291))
% 54.31/54.57  (step t293 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))))) :rule contraction :premises (t292))
% 54.31/54.57  (step t294 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) :rule implies :premises (t293))
% 54.31/54.57  (step t295 (cl (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)))) :rule resolution :premises (t294 a3))
% 54.31/54.57  (step t296 (cl (=> (forall ((X $$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 $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) :rule implies_neg1)
% 54.31/54.57  (anchor :step t297)
% 54.31/54.57  (assume t297.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))))
% 54.31/54.57  (step t297.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) :rule forall_inst :args ((:= X tptp.identity) (:= Y tptp.a)))
% 54.31/54.57  (step t297.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) :rule or :premises (t297.t1))
% 54.31/54.57  (step t297.t3 (cl (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) :rule resolution :premises (t297.t2 t297.a0))
% 54.31/54.57  (step t297 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) :rule subproof :discharge (t297.a0))
% 54.31/54.57  (step t298 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) :rule resolution :premises (t296 t297))
% 54.31/54.57  (step t299 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) :rule implies_neg2)
% 54.31/54.57  (step t300 (cl (=> (forall ((X $$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 $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) :rule resolution :premises (t298 t299))
% 54.31/54.57  (step t301 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) :rule contraction :premises (t300))
% 54.31/54.57  (step t302 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) :rule implies :premises (t301))
% 54.31/54.57  (step t303 (cl (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) :rule resolution :premises (t302 t234))
% 54.31/54.57  (step t304 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) :rule implies_neg1)
% 54.31/54.57  (anchor :step t305)
% 54.31/54.57  (assume t305.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))))
% 54.31/54.57  (step t305.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))))) :rule forall_inst :args ((:= X tptp.identity) (:= Y (tptp.inverse tptp.a))))
% 54.31/54.57  (step t305.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) :rule or :premises (t305.t1))
% 54.31/54.57  (step t305.t3 (cl (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) :rule resolution :premises (t305.t2 t305.a0))
% 54.31/54.57  (step t305 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) :rule subproof :discharge (t305.a0))
% 54.31/54.57  (step t306 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) :rule resolution :premises (t304 t305))
% 54.31/54.57  (step t307 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))))) :rule implies_neg2)
% 54.31/54.57  (step t308 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))))) :rule resolution :premises (t306 t307))
% 54.31/54.57  (step t309 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))))) :rule contraction :premises (t308))
% 54.31/54.57  (step t310 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) :rule implies :premises (t309))
% 54.31/54.57  (step t311 (cl (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) :rule resolution :premises (t310 t245))
% 54.31/54.57  (step t312 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z))))) :rule implies_neg1)
% 54.31/54.57  (anchor :step t313)
% 54.31/54.57  (assume t313.a0 (forall ((X $$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)))))
% 54.31/54.57  (step t313.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.a)) (:= Y tptp.a) (:= Z (tptp.greatest_lower_bound tptp.a tptp.identity))))
% 54.31/54.57  (step t313.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule or :premises (t313.t1))
% 54.31/54.57  (step t313.t3 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule resolution :premises (t313.t2 t313.a0))
% 54.31/54.57  (step t313 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule subproof :discharge (t313.a0))
% 54.31/54.57  (step t314 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule resolution :premises (t312 t313))
% 54.31/54.57  (step t315 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule implies_neg2)
% 54.31/54.57  (step t316 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule resolution :premises (t314 t315))
% 54.31/54.57  (step t317 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule contraction :premises (t316))
% 54.31/54.57  (step t318 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule implies :premises (t317))
% 54.31/54.57  (step t319 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule resolution :premises (t318 a11))
% 54.31/54.57  (step t320 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) :rule implies_neg1)
% 54.31/54.57  (anchor :step t321)
% 54.31/54.57  (assume t321.a0 (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))))
% 54.31/54.57  (step t321.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)))) :rule forall_inst :args ((:= X tptp.a)))
% 54.31/54.57  (step t321.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) :rule or :premises (t321.t1))
% 54.31/54.57  (step t321.t3 (cl (= tptp.a (tptp.multiply tptp.identity tptp.a))) :rule resolution :premises (t321.t2 t321.a0))
% 54.31/54.57  (step t321 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) :rule subproof :discharge (t321.a0))
% 54.31/54.57  (step t322 (cl (=> (forall ((X $$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 (t320 t321))
% 54.31/54.57  (step t323 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a)))) :rule implies_neg2)
% 54.31/54.57  (step t324 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.a (tptp.multiply tptp.identity tptp.a)))) :rule resolution :premises (t322 t323))
% 54.31/54.57  (step t325 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.a (tptp.multiply tptp.identity tptp.a)))) :rule contraction :premises (t324))
% 54.31/54.57  (step t326 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) :rule implies :premises (t325))
% 54.31/54.57  (step t327 (cl (= tptp.a (tptp.multiply tptp.identity tptp.a))) :rule resolution :premises (t326 t256))
% 54.31/54.57  (step t328 (cl (=> (forall ((X $$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 $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) :rule implies_neg1)
% 54.31/54.57  (anchor :step t329)
% 54.31/54.57  (assume t329.a0 (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))))
% 54.31/54.57  (step t329.t1 (cl (or (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.a))))
% 54.31/54.57  (step t329.t2 (cl (not (forall ((X $$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 (t329.t1))
% 54.31/54.57  (step t329.t3 (cl (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule resolution :premises (t329.t2 t329.a0))
% 54.31/54.57  (step t329 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule subproof :discharge (t329.a0))
% 54.31/54.57  (step t330 (cl (=> (forall ((X $$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 (t328 t329))
% 54.31/54.57  (step t331 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule implies_neg2)
% 54.31/54.57  (step t332 (cl (=> (forall ((X $$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 $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule resolution :premises (t330 t331))
% 54.31/54.57  (step t333 (cl (=> (forall ((X $$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 (t332))
% 54.31/54.57  (step t334 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule implies :premises (t333))
% 54.31/54.57  (step t335 (cl (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule resolution :premises (t334 t199))
% 54.31/54.57  (step t336 (cl (=> (forall ((X $$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.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z))))) :rule implies_neg1)
% 54.31/54.57  (anchor :step t337)
% 54.31/54.57  (assume t337.a0 (forall ((X $$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)))))
% 54.31/54.57  (step t337.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))))) :rule forall_inst :args ((:= X tptp.identity) (:= Y tptp.identity) (:= Z tptp.a)))
% 54.31/54.57  (step t337.t2 (cl (not (forall ((X $$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.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) :rule or :premises (t337.t1))
% 54.31/54.57  (step t337.t3 (cl (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) :rule resolution :premises (t337.t2 t337.a0))
% 54.31/54.57  (step t337 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) :rule subproof :discharge (t337.a0))
% 54.31/54.57  (step t338 (cl (=> (forall ((X $$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.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) :rule resolution :premises (t336 t337))
% 54.31/54.57  (step t339 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))))) :rule implies_neg2)
% 54.31/54.57  (step t340 (cl (=> (forall ((X $$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.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))))) :rule resolution :premises (t338 t339))
% 54.31/54.57  (step t341 (cl (=> (forall ((X $$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.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a))))) :rule contraction :premises (t340))
% 54.31/54.57  (step t342 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) :rule implies :premises (t341))
% 54.31/54.57  (step t343 (cl (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.identity tptp.a)))) :rule resolution :premises (t342 a12))
% 54.31/54.57  (step t344 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) :rule implies_neg1)
% 54.31/54.57  (anchor :step t345)
% 54.31/54.57  (assume t345.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))))
% 54.31/54.57  (step t345.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)))) :rule forall_inst :args ((:= X tptp.identity) (:= Y (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))))
% 54.31/54.57  (step t345.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) :rule or :premises (t345.t1))
% 54.31/54.57  (step t345.t3 (cl (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) :rule resolution :premises (t345.t2 t345.a0))
% 54.31/54.57  (step t345 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) :rule subproof :discharge (t345.a0))
% 54.31/54.57  (step t346 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) :rule resolution :premises (t344 t345))
% 54.31/54.57  (step t347 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)))) :rule implies_neg2)
% 54.31/54.57  (step t348 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)))) :rule resolution :premises (t346 t347))
% 54.31/54.57  (step t349 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)))) :rule contraction :premises (t348))
% 54.31/54.57  (step t350 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) :rule implies :premises (t349))
% 54.31/54.57  (step t351 (cl (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) :rule resolution :premises (t350 a3))
% 54.31/54.57  (step t352 (cl (=> (forall ((X $$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 $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 54.31/54.57  (anchor :step t353)
% 54.31/54.57  (assume t353.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 54.31/54.57  (step t353.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule forall_inst :args ((:= X (tptp.inverse (tptp.inverse tptp.a))) (:= Y (tptp.inverse tptp.a)) (:= Z tptp.a)))
% 54.31/54.57  (step t353.t2 (cl (not (forall ((X $$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 (t353.t1))
% 54.31/54.57  (step t353.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 (t353.t2 t353.a0))
% 54.31/54.57  (step t353 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule subproof :discharge (t353.a0))
% 54.31/54.57  (step t354 (cl (=> (forall ((X $$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 (t352 t353))
% 54.31/54.57  (step t355 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule implies_neg2)
% 54.31/54.57  (step t356 (cl (=> (forall ((X $$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 $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule resolution :premises (t354 t355))
% 54.31/54.57  (step t357 (cl (=> (forall ((X $$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 (t356))
% 54.31/54.57  (step t358 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule implies :premises (t357))
% 54.31/54.57  (step t359 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule resolution :premises (t358 a2))
% 54.31/54.57  (step t360 (cl (=> (forall ((X $$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.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 54.31/54.57  (anchor :step t361)
% 54.31/54.57  (assume t361.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 54.31/54.57  (step t361.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))))) :rule forall_inst :args ((:= X (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (:= Y tptp.identity) (:= Z (tptp.greatest_lower_bound tptp.identity tptp.a))))
% 54.31/54.57  (step t361.t2 (cl (not (forall ((X $$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.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) :rule or :premises (t361.t1))
% 54.31/54.57  (step t361.t3 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) :rule resolution :premises (t361.t2 t361.a0))
% 54.31/54.57  (step t361 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) :rule subproof :discharge (t361.a0))
% 54.31/54.57  (step t362 (cl (=> (forall ((X $$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.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) :rule resolution :premises (t360 t361))
% 54.31/54.57  (step t363 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))))) :rule implies_neg2)
% 54.31/54.57  (step t364 (cl (=> (forall ((X $$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.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))))) :rule resolution :premises (t362 t363))
% 54.31/54.57  (step t365 (cl (=> (forall ((X $$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.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))))) :rule contraction :premises (t364))
% 54.31/54.57  (step t366 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) :rule implies :premises (t365))
% 54.31/54.57  (step t367 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) :rule resolution :premises (t366 a2))
% 54.31/54.57  (step t368 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) :rule implies_neg1)
% 54.31/54.57  (anchor :step t369)
% 54.31/54.57  (assume t369.a0 (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))))
% 54.31/54.57  (step t369.t1 (cl (or (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule forall_inst :args ((:= Y (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (:= Z (tptp.inverse tptp.a)) (:= X tptp.a)))
% 54.31/54.57  (step t369.t2 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule or :premises (t369.t1))
% 54.31/54.57  (step t369.t3 (cl (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule resolution :premises (t369.t2 t369.a0))
% 54.31/54.57  (step t369 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule subproof :discharge (t369.a0))
% 54.31/54.57  (step t370 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule resolution :premises (t368 t369))
% 54.31/54.57  (step t371 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule implies_neg2)
% 54.31/54.57  (step t372 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule resolution :premises (t370 t371))
% 54.31/54.57  (step t373 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule contraction :premises (t372))
% 54.31/54.57  (step t374 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule implies :premises (t373))
% 54.31/54.57  (step t375 (cl (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule resolution :premises (t374 a14))
% 54.31/54.57  (step t376 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) :rule implies_neg1)
% 54.31/54.57  (anchor :step t377)
% 54.31/54.57  (assume t377.a0 (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))))
% 54.31/54.57  (step t377.t1 (cl (or (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))))) :rule forall_inst :args ((:= Y (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (:= Z tptp.identity) (:= X tptp.identity)))
% 54.31/54.57  (step t377.t2 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) :rule or :premises (t377.t1))
% 54.31/54.57  (step t377.t3 (cl (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) :rule resolution :premises (t377.t2 t377.a0))
% 54.31/54.57  (step t377 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) :rule subproof :discharge (t377.a0))
% 54.31/54.57  (step t378 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) :rule resolution :premises (t376 t377))
% 54.31/54.57  (step t379 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))))) :rule implies_neg2)
% 54.31/54.57  (step t380 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))))) :rule resolution :premises (t378 t379))
% 54.31/54.57  (step t381 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))))) :rule contraction :premises (t380))
% 54.31/54.57  (step t382 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) :rule implies :premises (t381))
% 54.31/54.57  (step t383 (cl (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) :rule resolution :premises (t382 a14))
% 54.31/54.57  (step t384 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) :rule implies_neg1)
% 54.31/54.57  (anchor :step t385)
% 54.31/54.57  (assume t385.a0 (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))))
% 54.31/54.57  (step t385.t1 (cl (or (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule forall_inst :args ((:= Y tptp.identity) (:= Z (tptp.inverse tptp.a)) (:= X tptp.a)))
% 54.31/54.57  (step t385.t2 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule or :premises (t385.t1))
% 54.31/54.57  (step t385.t3 (cl (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule resolution :premises (t385.t2 t385.a0))
% 54.31/54.57  (step t385 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule subproof :discharge (t385.a0))
% 54.31/54.57  (step t386 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule resolution :premises (t384 t385))
% 54.31/54.57  (step t387 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule implies_neg2)
% 54.31/54.57  (step t388 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule resolution :premises (t386 t387))
% 54.31/54.57  (step t389 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule contraction :premises (t388))
% 54.31/54.57  (step t390 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule implies :premises (t389))
% 54.31/54.57  (step t391 (cl (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule resolution :premises (t390 a14))
% 54.31/54.57  (step t392 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z)))) :rule implies_neg1)
% 54.31/54.57  (anchor :step t393)
% 54.31/54.57  (assume t393.a0 (forall ((X $$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))))
% 54.31/54.57  (step t393.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))))) :rule forall_inst :args ((:= X (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (:= Y (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (:= Z (tptp.greatest_lower_bound tptp.identity tptp.a))))
% 54.31/54.57  (step t393.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) :rule or :premises (t393.t1))
% 54.31/54.57  (step t393.t3 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) :rule resolution :premises (t393.t2 t393.a0))
% 54.31/54.57  (step t393 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) :rule subproof :discharge (t393.a0))
% 54.31/54.57  (step t394 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) :rule resolution :premises (t392 t393))
% 54.31/54.57  (step t395 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))))) :rule implies_neg2)
% 54.31/54.57  (step t396 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))))) :rule resolution :premises (t394 t395))
% 54.31/54.57  (step t397 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a))))) :rule contraction :premises (t396))
% 54.31/54.57  (step t398 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) :rule implies :premises (t397))
% 54.31/54.57  (step t399 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound tptp.identity tptp.a)))) :rule resolution :premises (t398 a6))
% 54.31/54.57  (step t400 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z))))) :rule implies_neg1)
% 54.31/54.57  (anchor :step t401)
% 54.31/54.57  (assume t401.a0 (forall ((X $$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)))))
% 54.31/54.57  (step t401.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.a)) (:= Y tptp.a) (:= Z tptp.identity)))
% 54.31/54.57  (step t401.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) :rule or :premises (t401.t1))
% 54.31/54.57  (step t401.t3 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) :rule resolution :premises (t401.t2 t401.a0))
% 54.31/54.57  (step t401 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) :rule subproof :discharge (t401.a0))
% 54.31/54.57  (step t402 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) :rule resolution :premises (t400 t401))
% 54.31/54.57  (step t403 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))))) :rule implies_neg2)
% 54.31/54.57  (step t404 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))))) :rule resolution :premises (t402 t403))
% 54.31/54.57  (step t405 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))))) :rule contraction :premises (t404))
% 54.31/54.57  (step t406 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) :rule implies :premises (t405))
% 54.31/54.57  (step t407 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) :rule resolution :premises (t406 a12))
% 54.31/54.57  (step t408 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) :rule implies_neg1)
% 54.31/54.57  (anchor :step t409)
% 54.31/54.57  (assume t409.a0 (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))))
% 54.31/54.57  (step t409.t1 (cl (or (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))))) :rule forall_inst :args ((:= Y tptp.identity) (:= Z tptp.a) (:= X tptp.identity)))
% 54.31/54.57  (step t409.t2 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) :rule or :premises (t409.t1))
% 54.31/54.57  (step t409.t3 (cl (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) :rule resolution :premises (t409.t2 t409.a0))
% 54.31/54.57  (step t409 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) :rule subproof :discharge (t409.a0))
% 54.31/54.57  (step t410 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) :rule resolution :premises (t408 t409))
% 54.31/54.57  (step t411 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))))) :rule implies_neg2)
% 54.31/54.57  (step t412 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))))) :rule resolution :premises (t410 t411))
% 54.31/54.57  (step t413 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity))))) :rule contraction :premises (t412))
% 54.31/54.57  (step t414 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) :rule implies :premises (t413))
% 54.31/54.57  (step t415 (cl (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.identity tptp.identity) (tptp.multiply tptp.a tptp.identity)))) :rule resolution :premises (t414 a14))
% 54.31/54.57  (step t416 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) :rule implies_neg1)
% 54.31/54.57  (anchor :step t417)
% 54.31/54.57  (assume t417.a0 (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))))
% 54.31/54.57  (step t417.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.a))))
% 54.31/54.57  (step t417.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) :rule or :premises (t417.t1))
% 54.31/54.57  (step t417.t3 (cl (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) :rule resolution :premises (t417.t2 t417.a0))
% 54.31/54.57  (step t417 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) :rule subproof :discharge (t417.a0))
% 54.31/54.57  (step t418 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) :rule resolution :premises (t416 t417))
% 54.31/54.57  (step t419 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) :rule implies_neg2)
% 54.31/54.57  (step t420 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) :rule resolution :premises (t418 t419))
% 54.31/54.57  (step t421 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) :rule contraction :premises (t420))
% 54.31/54.57  (step t422 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) :rule implies :premises (t421))
% 54.31/54.57  (step t423 (cl (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) :rule resolution :premises (t422 t256))
% 54.31/54.57  (step t424 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) :rule implies_neg1)
% 54.31/54.57  (anchor :step t425)
% 54.31/54.57  (assume t425.a0 (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))))
% 54.31/54.57  (step t425.t1 (cl (or (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule forall_inst :args ((:= X (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))
% 54.31/54.57  (step t425.t2 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule or :premises (t425.t1))
% 54.31/54.57  (step t425.t3 (cl (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule resolution :premises (t425.t2 t425.a0))
% 54.31/54.57  (step t425 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule subproof :discharge (t425.a0))
% 54.31/54.57  (step t426 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule resolution :premises (t424 t425))
% 54.31/54.57  (step t427 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule implies_neg2)
% 54.31/54.57  (step t428 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule resolution :premises (t426 t427))
% 54.31/54.57  (step t429 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule contraction :premises (t428))
% 54.31/54.57  (step t430 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule implies :premises (t429))
% 54.31/54.57  (step t431 (cl (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule resolution :premises (t430 t199))
% 54.31/54.57  (step t432 (cl (not (= (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule equiv_pos2)
% 54.31/54.57  (step t433 (cl (= (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))) :rule refl)
% 54.31/54.57  (step t434 (cl (= (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule all_simplify)
% 54.31/54.57  (step t435 (cl (= (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule cong :premises (t433 t434))
% 54.31/54.57  (step t436 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 54.31/54.57  (anchor :step t437)
% 54.31/54.57  (assume t437.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 54.31/54.57  (step t437.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule forall_inst :args ((:= X tptp.identity) (:= Y (tptp.inverse tptp.a)) (:= Z (tptp.greatest_lower_bound tptp.a tptp.identity))))
% 54.31/54.57  (step t437.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule or :premises (t437.t1))
% 54.31/54.57  (step t437.t3 (cl (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule resolution :premises (t437.t2 t437.a0))
% 54.31/54.57  (step t437 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule subproof :discharge (t437.a0))
% 54.31/54.57  (step t438 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule resolution :premises (t436 t437))
% 54.31/54.57  (step t439 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule implies_neg2)
% 54.31/54.57  (step t440 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule resolution :premises (t438 t439))
% 54.31/54.57  (step t441 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule contraction :premises (t440))
% 54.31/54.57  (step t442 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule resolution :premises (t432 t435 t441))
% 54.31/54.57  (step t443 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule implies :premises (t442))
% 54.31/54.57  (step t444 (cl (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule resolution :premises (t443 a2))
% 54.31/54.57  (step t445 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 54.31/54.57  (anchor :step t446)
% 54.31/54.57  (assume t446.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 54.31/54.57  (step t446.t1 (cl (or (not (forall ((X $$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.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))))) :rule forall_inst :args ((:= X (tptp.inverse (tptp.inverse tptp.a))) (:= Y (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (:= Z tptp.identity)))
% 54.31/54.57  (step t446.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) :rule or :premises (t446.t1))
% 54.31/54.57  (step t446.t3 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) :rule resolution :premises (t446.t2 t446.a0))
% 54.31/54.57  (step t446 (cl (not (forall ((X $$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.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) :rule subproof :discharge (t446.a0))
% 54.31/54.57  (step t447 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) :rule resolution :premises (t445 t446))
% 54.31/54.57  (step t448 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))))) :rule implies_neg2)
% 54.31/54.57  (step t449 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) (=> (forall ((X $$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.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))))) :rule resolution :premises (t447 t448))
% 54.31/54.57  (step t450 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))))) :rule contraction :premises (t449))
% 54.31/54.57  (step t451 (cl (not (forall ((X $$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.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) :rule implies :premises (t450))
% 54.31/54.57  (step t452 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)))) :rule resolution :premises (t451 a2))
% 54.31/54.57  (step t453 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (forall ((Y $$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)
% 54.31/54.57  (anchor :step t454)
% 54.31/54.57  (assume t454.a0 (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))))
% 54.31/54.57  (step t454.t1 (cl (or (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a)) (:= Z tptp.identity) (:= X (tptp.greatest_lower_bound tptp.a tptp.identity))))
% 54.31/54.57  (step t454.t2 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule or :premises (t454.t1))
% 54.31/54.57  (step t454.t3 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule resolution :premises (t454.t2 t454.a0))
% 54.31/54.57  (step t454 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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 (t454.a0))
% 54.31/54.57  (step t455 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule resolution :premises (t453 t454))
% 54.31/54.57  (step t456 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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)
% 54.31/54.57  (step t457 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) (=> (forall ((Y $$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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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 (t455 t456))
% 54.31/54.57  (step t458 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule contraction :premises (t457))
% 54.31/54.57  (step t459 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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 (t458))
% 54.31/54.57  (step t460 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse 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 (t459 a13))
% 54.31/54.57  (step t461 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) :rule implies_neg1)
% 54.31/54.57  (anchor :step t462)
% 54.31/54.57  (assume t462.a0 (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))))
% 54.31/54.57  (step t462.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule forall_inst :args ((:= X (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))
% 54.31/54.57  (step t462.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule or :premises (t462.t1))
% 54.31/54.57  (step t462.t3 (cl (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule resolution :premises (t462.t2 t462.a0))
% 54.31/54.57  (step t462 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule subproof :discharge (t462.a0))
% 54.31/54.57  (step t463 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule resolution :premises (t461 t462))
% 54.31/54.57  (step t464 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule implies_neg2)
% 54.31/54.57  (step t465 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule resolution :premises (t463 t464))
% 54.31/54.57  (step t466 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule contraction :premises (t465))
% 54.31/54.57  (step t467 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule implies :premises (t466))
% 54.31/54.57  (step t468 (cl (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule resolution :premises (t467 t256))
% 54.31/54.57  (step t469 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 54.31/54.57  (anchor :step t470)
% 54.31/54.57  (assume t470.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 54.31/54.57  (step t470.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))))) :rule forall_inst :args ((:= X tptp.identity) (:= Y (tptp.inverse tptp.a)) (:= Z tptp.identity)))
% 54.31/54.57  (step t470.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) :rule or :premises (t470.t1))
% 54.31/54.57  (step t470.t3 (cl (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) :rule resolution :premises (t470.t2 t470.a0))
% 54.31/54.57  (step t470 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) :rule subproof :discharge (t470.a0))
% 54.31/54.57  (step t471 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) :rule resolution :premises (t469 t470))
% 54.31/54.57  (step t472 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))))) :rule implies_neg2)
% 54.31/54.57  (step t473 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))))) :rule resolution :premises (t471 t472))
% 54.31/54.57  (step t474 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity))))) :rule contraction :premises (t473))
% 54.31/54.57  (step t475 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) :rule implies :premises (t474))
% 54.31/54.57  (step t476 (cl (= (tptp.multiply (tptp.multiply tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) :rule resolution :premises (t475 a2))
% 54.31/54.57  (step t477 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 54.31/54.57  (anchor :step t478)
% 54.31/54.57  (assume t478.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 54.31/54.57  (step t478.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))))) :rule forall_inst :args ((:= X (tptp.inverse (tptp.inverse tptp.a))) (:= Y tptp.identity) (:= Z (tptp.inverse tptp.a))))
% 54.31/54.57  (step t478.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) :rule or :premises (t478.t1))
% 54.31/54.57  (step t478.t3 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) :rule resolution :premises (t478.t2 t478.a0))
% 54.31/54.57  (step t478 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) :rule subproof :discharge (t478.a0))
% 54.31/54.57  (step t479 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) :rule resolution :premises (t477 t478))
% 54.31/54.57  (step t480 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))))) :rule implies_neg2)
% 54.31/54.57  (step t481 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))))) :rule resolution :premises (t479 t480))
% 54.31/54.57  (step t482 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))))) :rule contraction :premises (t481))
% 54.31/54.57  (step t483 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) :rule implies :premises (t482))
% 54.31/54.57  (step t484 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) :rule resolution :premises (t483 a2))
% 54.31/54.57  (step t485 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 54.31/54.57  (anchor :step t486)
% 54.31/54.57  (assume t486.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 54.31/54.57  (step t486.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.a)) (:= Y (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (:= Z (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))
% 54.31/54.57  (step t486.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule or :premises (t486.t1))
% 54.31/54.57  (step t486.t3 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule resolution :premises (t486.t2 t486.a0))
% 54.31/54.57  (step t486 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule subproof :discharge (t486.a0))
% 54.31/54.57  (step t487 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule resolution :premises (t485 t486))
% 54.31/54.57  (step t488 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))))) :rule implies_neg2)
% 54.31/54.57  (step t489 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))))) :rule resolution :premises (t487 t488))
% 54.31/54.57  (step t490 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))))) :rule contraction :premises (t489))
% 54.31/54.57  (step t491 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule implies :premises (t490))
% 54.31/54.57  (step t492 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule resolution :premises (t491 a2))
% 54.31/54.57  (step t493 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (forall ((X $$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)
% 54.31/54.57  (anchor :step t494)
% 54.31/54.57  (assume t494.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))))
% 54.31/54.57  (step t494.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))))) :rule forall_inst :args ((:= X (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (:= Y tptp.a) (:= Z tptp.identity)))
% 54.31/54.57  (step t494.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) :rule or :premises (t494.t1))
% 54.31/54.57  (step t494.t3 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) :rule resolution :premises (t494.t2 t494.a0))
% 54.31/54.57  (step t494 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) :rule subproof :discharge (t494.a0))
% 54.31/54.57  (step t495 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) :rule resolution :premises (t493 t494))
% 54.31/54.57  (step t496 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))))) :rule implies_neg2)
% 54.31/54.57  (step t497 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) (=> (forall ((X $$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.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))))) :rule resolution :premises (t495 t496))
% 54.31/54.57  (step t498 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity))))) :rule contraction :premises (t497))
% 54.31/54.57  (step t499 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) :rule implies :premises (t498))
% 54.31/54.57  (step t500 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)))) :rule resolution :premises (t499 a12))
% 54.31/54.57  (step t501 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (forall ((X $$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)
% 54.31/54.57  (anchor :step t502)
% 54.31/54.57  (assume t502.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))))
% 54.31/54.57  (step t502.t1 (cl (or (not (forall ((X $$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.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))))) :rule forall_inst :args ((:= X (tptp.greatest_lower_bound tptp.a tptp.identity)) (:= Y (tptp.inverse tptp.a)) (:= Z tptp.identity)))
% 54.31/54.57  (step t502.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) :rule or :premises (t502.t1))
% 54.31/54.57  (step t502.t3 (cl (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) :rule resolution :premises (t502.t2 t502.a0))
% 54.31/54.57  (step t502 (cl (not (forall ((X $$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.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) :rule subproof :discharge (t502.a0))
% 54.31/54.57  (step t503 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) :rule resolution :premises (t501 t502))
% 54.31/54.57  (step t504 (cl (=> (forall ((X $$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.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))))) :rule implies_neg2)
% 54.31/54.57  (step t505 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (=> (forall ((X $$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.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))))) :rule resolution :premises (t503 t504))
% 54.31/54.57  (step t506 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))))) :rule contraction :premises (t505))
% 54.31/54.57  (step t507 (cl (not (forall ((X $$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.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) :rule implies :premises (t506))
% 54.31/54.57  (step t508 (cl (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) :rule resolution :premises (t507 a11))
% 54.31/54.57  (step t509 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) :rule implies_neg1)
% 54.31/54.57  (anchor :step t510)
% 54.31/54.57  (assume t510.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))))
% 54.31/54.57  (step t510.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule forall_inst :args ((:= X (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (:= Y (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)))))
% 54.31/54.57  (step t510.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule or :premises (t510.t1))
% 54.31/54.57  (step t510.t3 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule resolution :premises (t510.t2 t510.a0))
% 54.31/54.57  (step t510 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule subproof :discharge (t510.a0))
% 54.31/54.57  (step t511 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule resolution :premises (t509 t510))
% 54.31/54.57  (step t512 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule implies_neg2)
% 54.31/54.57  (step t513 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse 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.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule resolution :premises (t511 t512))
% 54.31/54.57  (step t514 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule contraction :premises (t513))
% 54.31/54.57  (step t515 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule implies :premises (t514))
% 54.31/54.57  (step t516 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule resolution :premises (t515 a4))
% 54.31/54.57  (step t517 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) :rule implies_neg1)
% 54.31/54.57  (anchor :step t518)
% 54.31/54.57  (assume t518.a0 (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))))
% 54.31/54.57  (step t518.t1 (cl (or (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))))) :rule forall_inst :args ((:= Y (tptp.inverse tptp.a)) (:= Z tptp.identity) (:= X tptp.identity)))
% 54.31/54.57  (step t518.t2 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) :rule or :premises (t518.t1))
% 54.31/54.57  (step t518.t3 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) :rule resolution :premises (t518.t2 t518.a0))
% 54.31/54.57  (step t518 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) :rule subproof :discharge (t518.a0))
% 54.31/54.57  (step t519 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) :rule resolution :premises (t517 t518))
% 54.31/54.57  (step t520 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))))) :rule implies_neg2)
% 54.31/54.57  (step t521 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))))) :rule resolution :premises (t519 t520))
% 54.31/54.57  (step t522 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity))))) :rule contraction :premises (t521))
% 54.31/54.57  (step t523 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) :rule implies :premises (t522))
% 54.31/54.57  (step t524 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.identity tptp.identity)))) :rule resolution :premises (t523 a13))
% 54.31/54.57  (step t525 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) :rule implies_neg1)
% 54.31/54.57  (anchor :step t526)
% 54.31/54.57  (assume t526.a0 (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))))
% 54.31/54.57  (step t526.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule forall_inst :args ((:= X (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))
% 54.31/54.57  (step t526.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule or :premises (t526.t1))
% 54.31/54.57  (step t526.t3 (cl (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule resolution :premises (t526.t2 t526.a0))
% 54.31/54.57  (step t526 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule subproof :discharge (t526.a0))
% 54.31/54.57  (step t527 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule resolution :premises (t525 t526))
% 54.31/54.57  (step t528 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule implies_neg2)
% 54.31/54.57  (step t529 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule resolution :premises (t527 t528))
% 54.31/54.57  (step t530 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule contraction :premises (t529))
% 54.31/54.57  (step t531 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule implies :premises (t530))
% 54.31/54.57  (step t532 (cl (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule resolution :premises (t531 t256))
% 54.31/54.57  (step t533 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) :rule implies_neg1)
% 54.31/54.57  (anchor :step t534)
% 54.31/54.57  (assume t534.a0 (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))))
% 54.31/54.57  (step t534.t1 (cl (or (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule forall_inst :args ((:= X (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))
% 54.31/54.57  (step t534.t2 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule or :premises (t534.t1))
% 54.31/54.57  (step t534.t3 (cl (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule resolution :premises (t534.t2 t534.a0))
% 54.31/54.57  (step t534 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule subproof :discharge (t534.a0))
% 54.31/54.57  (step t535 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule resolution :premises (t533 t534))
% 54.31/54.57  (step t536 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule implies_neg2)
% 54.31/54.57  (step t537 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule resolution :premises (t535 t536))
% 54.31/54.57  (step t538 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule contraction :premises (t537))
% 54.31/54.57  (step t539 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule implies :premises (t538))
% 54.31/54.57  (step t540 (cl (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule resolution :premises (t539 t199))
% 54.31/54.57  (step t541 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 54.31/54.57  (anchor :step t542)
% 54.31/54.57  (assume t542.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 54.31/54.57  (step t542.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.a)) (:= Y tptp.a) (:= Z (tptp.inverse tptp.a))))
% 54.31/54.57  (step t542.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule or :premises (t542.t1))
% 54.31/54.57  (step t542.t3 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule resolution :premises (t542.t2 t542.a0))
% 54.31/54.57  (step t542 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule subproof :discharge (t542.a0))
% 54.31/54.57  (step t543 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule resolution :premises (t541 t542))
% 54.31/54.57  (step t544 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) :rule implies_neg2)
% 54.31/54.57  (step t545 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) :rule resolution :premises (t543 t544))
% 54.31/54.57  (step t546 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) :rule contraction :premises (t545))
% 54.31/54.57  (step t547 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule implies :premises (t546))
% 54.31/54.57  (step t548 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule resolution :premises (t547 a2))
% 54.31/54.57  (step t549 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 54.31/54.57  (anchor :step t550)
% 54.31/54.57  (assume t550.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 54.31/54.57  (step t550.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) :rule forall_inst :args ((:= X (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (:= Y tptp.a) (:= Z (tptp.inverse tptp.a))))
% 54.31/54.57  (step t550.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule or :premises (t550.t1))
% 54.31/54.57  (step t550.t3 (cl (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule resolution :premises (t550.t2 t550.a0))
% 54.31/54.57  (step t550 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule subproof :discharge (t550.a0))
% 54.31/54.57  (step t551 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule resolution :premises (t549 t550))
% 54.31/54.57  (step t552 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) :rule implies_neg2)
% 54.31/54.57  (step t553 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) :rule resolution :premises (t551 t552))
% 54.31/54.57  (step t554 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) :rule contraction :premises (t553))
% 54.31/54.57  (step t555 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule implies :premises (t554))
% 54.31/54.57  (step t556 (cl (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule resolution :premises (t555 a2))
% 54.31/54.57  (step t557 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 54.31/54.57  (anchor :step t558)
% 54.31/54.57  (assume t558.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 54.31/54.57  (step t558.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.a)) (:= Y (tptp.greatest_lower_bound tptp.a tptp.identity)) (:= Z tptp.identity)))
% 54.31/54.57  (step t558.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) :rule or :premises (t558.t1))
% 54.31/54.57  (step t558.t3 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) :rule resolution :premises (t558.t2 t558.a0))
% 54.31/54.57  (step t558 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) :rule subproof :discharge (t558.a0))
% 54.31/54.57  (step t559 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) :rule resolution :premises (t557 t558))
% 54.31/54.57  (step t560 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))))) :rule implies_neg2)
% 54.31/54.57  (step t561 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))))) :rule resolution :premises (t559 t560))
% 54.31/54.57  (step t562 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity))))) :rule contraction :premises (t561))
% 54.31/54.57  (step t563 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) :rule implies :premises (t562))
% 54.31/54.57  (step t564 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.identity)))) :rule resolution :premises (t563 a2))
% 54.31/54.57  (step t565 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (forall ((X $$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)
% 54.31/54.57  (anchor :step t566)
% 54.31/54.57  (assume t566.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z))))
% 54.31/54.57  (step t566.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))))) :rule forall_inst :args ((:= X (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (:= Y (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (:= Z (tptp.multiply tptp.identity tptp.identity))))
% 54.31/54.57  (step t566.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) :rule or :premises (t566.t1))
% 54.31/54.57  (step t566.t3 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) :rule resolution :premises (t566.t2 t566.a0))
% 54.31/54.57  (step t566 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) :rule subproof :discharge (t566.a0))
% 54.31/54.57  (step t567 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) :rule resolution :premises (t565 t566))
% 54.31/54.57  (step t568 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))))) :rule implies_neg2)
% 54.31/54.57  (step t569 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) (=> (forall ((X $$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.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))))) :rule resolution :premises (t567 t568))
% 54.31/54.57  (step t570 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity))))) :rule contraction :premises (t569))
% 54.31/54.57  (step t571 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) :rule implies :premises (t570))
% 54.31/54.57  (step t572 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity) (tptp.multiply tptp.identity tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.identity)) (tptp.multiply tptp.identity tptp.identity)))) :rule resolution :premises (t571 a5))
% 54.31/54.57  (step t573 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) :rule implies_neg1)
% 54.31/54.57  (anchor :step t574)
% 54.31/54.57  (assume t574.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))))
% 54.31/54.57  (step t574.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule forall_inst :args ((:= X (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity))) (:= Y (tptp.multiply (tptp.inverse tptp.a) tptp.a))))
% 54.31/54.57  (step t574.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule or :premises (t574.t1))
% 54.31/54.57  (step t574.t3 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule resolution :premises (t574.t2 t574.a0))
% 54.31/54.57  (step t574 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule subproof :discharge (t574.a0))
% 54.31/54.57  (step t575 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule resolution :premises (t573 t574))
% 54.31/54.57  (step t576 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule implies_neg2)
% 54.31/54.57  (step t577 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule resolution :premises (t575 t576))
% 54.31/54.57  (step t578 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule contraction :premises (t577))
% 54.31/54.57  (step t579 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule implies :premises (t578))
% 54.31/54.57  (step t580 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule resolution :premises (t579 t245))
% 54.31/54.57  (step t581 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 54.31/54.57  (anchor :step t582)
% 54.31/54.57  (assume t582.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 54.31/54.57  (step t582.t1 (cl (or (not (forall ((X $$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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))))) :rule forall_inst :args ((:= X (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (:= Y (tptp.greatest_lower_bound tptp.a tptp.identity)) (:= Z (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))
% 54.31/54.57  (step t582.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule or :premises (t582.t1))
% 54.31/54.57  (step t582.t3 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule resolution :premises (t582.t2 t582.a0))
% 54.31/54.57  (step t582 (cl (not (forall ((X $$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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule subproof :discharge (t582.a0))
% 54.31/54.57  (step t583 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule resolution :premises (t581 t582))
% 54.31/54.57  (step t584 (cl (=> (forall ((X $$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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))))) :rule implies_neg2)
% 54.31/54.57  (step t585 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (=> (forall ((X $$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.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))))) :rule resolution :premises (t583 t584))
% 54.31/54.57  (step t586 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))))) :rule contraction :premises (t585))
% 54.31/54.57  (step t587 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule implies :premises (t586))
% 54.31/54.57  (step t588 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule resolution :premises (t587 a2))
% 54.31/54.57  (step t589 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 54.31/54.57  (anchor :step t590)
% 54.31/54.57  (assume t590.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 54.31/54.57  (step t590.t1 (cl (or (not (forall ((X $$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.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))))) :rule forall_inst :args ((:= X (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (:= Y (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (:= Z tptp.identity)))
% 54.31/54.57  (step t590.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) :rule or :premises (t590.t1))
% 54.31/54.57  (step t590.t3 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) :rule resolution :premises (t590.t2 t590.a0))
% 54.31/54.57  (step t590 (cl (not (forall ((X $$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.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) :rule subproof :discharge (t590.a0))
% 54.31/54.57  (step t591 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) :rule resolution :premises (t589 t590))
% 54.31/54.57  (step t592 (cl (=> (forall ((X $$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.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))))) :rule implies_neg2)
% 54.31/54.57  (step t593 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (=> (forall ((X $$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.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))))) :rule resolution :premises (t591 t592))
% 54.31/54.57  (step t594 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))))) :rule contraction :premises (t593))
% 54.31/54.57  (step t595 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) :rule implies :premises (t594))
% 54.31/54.57  (step t596 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) :rule resolution :premises (t595 a2))
% 54.31/54.57  (step t597 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 54.31/54.57  (anchor :step t598)
% 54.31/54.57  (assume t598.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 54.31/54.57  (step t598.t1 (cl (or (not (forall ((X $$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.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) :rule forall_inst :args ((:= X (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (:= Y tptp.identity) (:= Z (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))
% 54.31/54.57  (step t598.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule or :premises (t598.t1))
% 54.31/54.57  (step t598.t3 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule resolution :premises (t598.t2 t598.a0))
% 54.31/54.57  (step t598 (cl (not (forall ((X $$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.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule subproof :discharge (t598.a0))
% 54.31/54.57  (step t599 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule resolution :premises (t597 t598))
% 54.31/54.57  (step t600 (cl (=> (forall ((X $$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.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) :rule implies_neg2)
% 54.31/54.57  (step t601 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (=> (forall ((X $$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.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) :rule resolution :premises (t599 t600))
% 54.31/54.57  (step t602 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) :rule contraction :premises (t601))
% 54.31/54.57  (step t603 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule implies :premises (t602))
% 54.31/54.57  (step t604 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule resolution :premises (t603 a2))
% 54.31/54.57  (step t605 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 54.31/54.57  (anchor :step t606)
% 54.31/54.57  (assume t606.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 54.31/54.57  (step t606.t1 (cl (or (not (forall ((X $$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.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) :rule forall_inst :args ((:= X (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (:= Y (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (:= Z (tptp.greatest_lower_bound tptp.identity tptp.a))))
% 54.31/54.57  (step t606.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) :rule or :premises (t606.t1))
% 54.31/54.57  (step t606.t3 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) :rule resolution :premises (t606.t2 t606.a0))
% 54.31/54.57  (step t606 (cl (not (forall ((X $$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.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) :rule subproof :discharge (t606.a0))
% 54.31/54.57  (step t607 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) :rule resolution :premises (t605 t606))
% 54.31/54.57  (step t608 (cl (=> (forall ((X $$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.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) :rule implies_neg2)
% 54.31/54.57  (step t609 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) :rule resolution :premises (t607 t608))
% 54.31/54.57  (step t610 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))))) :rule contraction :premises (t609))
% 54.31/54.57  (step t611 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) :rule implies :premises (t610))
% 54.31/54.57  (step t612 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))))) :rule resolution :premises (t611 a2))
% 54.31/54.57  (step t613 (cl (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) :rule resolution :premises (t189 a15 t200 t208 t216 t224 t235 t246 t257 t265 t276 t287 t295 t303 t311 t319 t327 t335 t343 t351 t359 t367 t375 t383 t391 t399 t407 t415 t423 t431 t444 t452 t460 t468 t476 t484 t492 t500 t508 t516 t524 t532 t540 t548 t556 t564 t572 t580 t588 t596 t604 t612))
% 54.31/54.57  (step t614 (cl) :rule resolution :premises (t7 t613 a2))
% 54.31/54.57  
% 54.31/54.58  % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.cyo0oJjqrY/cvc5---1.0.5_25890.smt2
% 54.35/54.58  % cvc5---1.0.5 exiting
% 54.35/54.58  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------