%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : GRP184-2 : TPTP v8.2.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : do_cvc5 %s %d

% Computer : n013.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed May 29 16:53:38 EDT 2024

% Result   : Unsatisfiable 30.71s 31.09s
% Output   : Proof 30.71s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : GRP184-2 : TPTP v8.2.0. Bugfixed v1.2.1.
% 0.14/0.14  % Command    : do_cvc5 %s %d
% 0.15/0.36  % Computer : n013.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Sun May 26 17:48:24 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.22/0.50  %----Proving TF0_NAR, FOF, or CNF
% 0.22/0.51  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.47/10.70  --- Run --no-e-matching --full-saturate-quant at 5...
% 15.47/15.73  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 20.55/20.76  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 25.53/25.78  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 30.66/30.90  --- Run --trigger-sel=max --full-saturate-quant at 5...
% 30.71/31.09  % SZS status Unsatisfiable for /export/starexec/sandbox/tmp/tmp.LGXdLJ4SQZ/cvc5---1.0.5_20700.smt2
% 30.71/31.09  % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.LGXdLJ4SQZ/cvc5---1.0.5_20700.smt2
% 30.71/31.13  (assume a0 (forall ((X $$unsorted)) (= (tptp.multiply tptp.identity X) X)))
% 30.71/31.13  (assume a1 (forall ((X $$unsorted)) (= (tptp.multiply (tptp.inverse X) X) tptp.identity)))
% 30.71/31.13  (assume a2 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 30.71/31.13  (assume a3 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))))
% 30.71/31.13  (assume a4 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))))
% 30.71/31.13  (assume a5 (forall ((X $$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))))
% 30.71/31.13  (assume a6 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))))
% 30.71/31.13  (assume a7 (forall ((X $$unsorted)) (= (tptp.least_upper_bound X X) X)))
% 30.71/31.13  (assume a8 (forall ((X $$unsorted)) (= (tptp.greatest_lower_bound X X) X)))
% 30.71/31.13  (assume a9 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)) X)))
% 30.71/31.13  (assume a10 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)) X)))
% 30.71/31.13  (assume a11 (forall ((X $$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)))))
% 30.71/31.13  (assume a12 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))))
% 30.71/31.13  (assume a13 (forall ((Y $$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)))))
% 30.71/31.13  (assume a14 (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))))
% 30.71/31.13  (assume a15 (= (tptp.inverse tptp.identity) tptp.identity))
% 30.71/31.13  (assume a16 (forall ((X $$unsorted)) (= (tptp.inverse (tptp.inverse X)) X)))
% 30.71/31.13  (assume a17 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))))
% 30.71/31.13  (assume a18 (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))))
% 30.71/31.13  (step t1 (cl (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= tptp.identity (tptp.inverse tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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)))))) (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.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a)))) (not (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound 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.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) :rule and_neg)
% 30.71/31.13  (step t2 (cl (=> (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) :rule implies_neg1)
% 30.71/31.13  (anchor :step t3)
% 30.71/31.13  (assume t3.a0 (= tptp.identity (tptp.inverse tptp.identity)))
% 30.71/31.13  (assume t3.a1 (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))
% 30.71/31.13  (assume t3.a2 (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))))
% 30.71/31.13  (assume t3.a3 (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))))
% 30.71/31.13  (assume t3.a4 (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))
% 30.71/31.13  (assume t3.a5 (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))))
% 30.71/31.13  (assume t3.a6 (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))
% 30.71/31.13  (assume t3.a7 (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))))
% 30.71/31.13  (assume t3.a8 (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))
% 30.71/31.13  (assume t3.a9 (= tptp.a (tptp.multiply tptp.identity tptp.a)))
% 30.71/31.13  (assume t3.a10 (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))
% 30.71/31.13  (assume t3.a11 (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))
% 30.71/31.13  (assume t3.a12 (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))))
% 30.71/31.13  (assume t3.a13 (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))))
% 30.71/31.13  (assume t3.a14 (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))
% 30.71/31.13  (assume t3.a15 (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))
% 30.71/31.13  (assume t3.a16 (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))
% 30.71/31.13  (assume t3.a17 (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))
% 30.71/31.13  (assume t3.a18 (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))
% 30.71/31.13  (step t3.t1 (cl (=> (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule implies_neg1)
% 30.71/31.13  (anchor :step t3.t2)
% 30.71/31.13  (assume t3.t2.a0 (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))
% 30.71/31.13  (assume t3.t2.a1 (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))
% 30.71/31.13  (assume t3.t2.a2 (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))))
% 30.71/31.13  (assume t3.t2.a3 (= tptp.a (tptp.multiply tptp.identity tptp.a)))
% 30.71/31.13  (assume t3.t2.a4 (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))
% 30.71/31.13  (assume t3.t2.a5 (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))
% 30.71/31.13  (assume t3.t2.a6 (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)))
% 30.71/31.13  (assume t3.t2.a7 (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))))
% 30.71/31.13  (assume t3.t2.a8 (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))
% 30.71/31.13  (assume t3.t2.a9 (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))))
% 30.71/31.13  (assume t3.t2.a10 (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))
% 30.71/31.13  (assume t3.t2.a11 (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))
% 30.71/31.13  (assume t3.t2.a12 (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))))
% 30.71/31.13  (assume t3.t2.a13 (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))))
% 30.71/31.13  (assume t3.t2.a14 (= tptp.identity (tptp.inverse tptp.identity)))
% 30.71/31.13  (assume t3.t2.a15 (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))
% 30.71/31.13  (assume t3.t2.a16 (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))
% 30.71/31.13  (assume t3.t2.a17 (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))))
% 30.71/31.13  (assume t3.t2.a18 (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))
% 30.71/31.13  (step t3.t2.t1 (cl (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule symm :premises (t3.t2.a12))
% 30.71/31.13  (step t3.t2.t2 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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 symm :premises (t3.t2.t1))
% 30.71/31.13  (step t3.t2.t3 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (tptp.least_upper_bound (tptp.multiply 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 symm :premises (t3.t2.a16))
% 30.71/31.13  (step t3.t2.t4 (cl (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule symm :premises (t3.t2.t3))
% 30.71/31.13  (step t3.t2.t5 (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 (t3.t2.a8))
% 30.71/31.13  (step t3.t2.t6 (cl (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound tptp.a tptp.identity))) :rule symm :premises (t3.t2.a15))
% 30.71/31.13  (step t3.t2.t7 (cl (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule symm :premises (t3.t2.t6))
% 30.71/31.13  (step t3.t2.t8 (cl (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule cong :premises (t3.t2.t7))
% 30.71/31.13  (step t3.t2.t9 (cl (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity)) (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule symm :premises (t3.t2.a9))
% 30.71/31.13  (step t3.t2.t10 (cl (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity)))) :rule symm :premises (t3.t2.t9))
% 30.71/31.13  (step t3.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)
% 30.71/31.13  (step t3.t2.t12 (cl (= (tptp.inverse tptp.identity) tptp.identity)) :rule symm :premises (t3.t2.a14))
% 30.71/31.13  (step t3.t2.t13 (cl (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) :rule cong :premises (t3.t2.t11 t3.t2.t12))
% 30.71/31.13  (step t3.t2.t14 (cl (= (tptp.multiply tptp.identity (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 (t3.t2.t5 t3.t2.t8 t3.t2.t10 t3.t2.t13))
% 30.71/31.13  (step t3.t2.t15 (cl (= tptp.a tptp.a)) :rule refl)
% 30.71/31.13  (step t3.t2.t16 (cl (= (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule cong :premises (t3.t2.t15 t3.t2.a8))
% 30.71/31.13  (step t3.t2.t17 (cl (= (tptp.multiply tptp.a (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule cong :premises (t3.t2.a5 t3.t2.t5))
% 30.71/31.13  (step t3.t2.t18 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))))) :rule symm :premises (t3.t2.a11))
% 30.71/31.13  (step t3.t2.t19 (cl (= (tptp.inverse tptp.a) (tptp.inverse tptp.a))) :rule refl)
% 30.71/31.13  (step t3.t2.t20 (cl (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)))) :rule cong :premises (t3.t2.a6 t3.t2.t19))
% 30.71/31.13  (step t3.t2.t21 (cl (= (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)))) :rule symm :premises (t3.t2.a10))
% 30.71/31.13  (step t3.t2.t22 (cl (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule symm :premises (t3.t2.t21))
% 30.71/31.13  (step t3.t2.t23 (cl (= (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) :rule symm :premises (t3.t2.a1))
% 30.71/31.13  (step t3.t2.t24 (cl (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule cong :premises (t3.t2.a5 t3.t2.t19))
% 30.71/31.13  (step t3.t2.t25 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.identity)) :rule symm :premises (t3.t2.a0))
% 30.71/31.13  (step t3.t2.t26 (cl (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.identity)) :rule trans :premises (t3.t2.t24 t3.t2.t25))
% 30.71/31.13  (step t3.t2.t27 (cl (= (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity))) :rule cong :premises (t3.t2.t23 t3.t2.t26))
% 30.71/31.13  (step t3.t2.t28 (cl (= (tptp.multiply tptp.identity tptp.a) tptp.a)) :rule symm :premises (t3.t2.a3))
% 30.71/31.13  (step t3.t2.t29 (cl (= tptp.a (tptp.multiply tptp.identity tptp.a))) :rule symm :premises (t3.t2.t28))
% 30.71/31.13  (step t3.t2.t30 (cl (= (tptp.inverse tptp.a) (tptp.inverse (tptp.multiply tptp.identity tptp.a)))) :rule cong :premises (t3.t2.t29))
% 30.71/31.13  (step t3.t2.t31 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity)) (tptp.inverse (tptp.multiply tptp.identity tptp.a)))) :rule symm :premises (t3.t2.a17))
% 30.71/31.13  (step t3.t2.t32 (cl (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity)))) :rule symm :premises (t3.t2.t31))
% 30.71/31.13  (step t3.t2.t33 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) :rule cong :premises (t3.t2.t19 t3.t2.t12))
% 30.71/31.13  (step t3.t2.t34 (cl (= (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) :rule trans :premises (t3.t2.t30 t3.t2.t32 t3.t2.t33))
% 30.71/31.13  (step t3.t2.t35 (cl (= (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)) :rule symm :premises (t3.t2.a18))
% 30.71/31.13  (step t3.t2.t36 (cl (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule symm :premises (t3.t2.t35))
% 30.71/31.13  (step t3.t2.t37 (cl (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule cong :premises (t3.t2.t34 t3.t2.t36))
% 30.71/31.13  (step t3.t2.t38 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)))) :rule symm :premises (t3.t2.a4))
% 30.71/31.13  (step t3.t2.t39 (cl (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) :rule symm :premises (t3.t2.a6))
% 30.71/31.13  (step t3.t2.t40 (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 (t3.t2.t19 t3.t2.t39))
% 30.71/31.13  (step t3.t2.t41 (cl (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule trans :premises (t3.t2.t20 t3.t2.t22 t3.t2.t27 t3.t2.t37 t3.t2.t38 t3.t2.t40))
% 30.71/31.13  (step t3.t2.t42 (cl (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule cong :premises (t3.t2.t41))
% 30.71/31.13  (step t3.t2.t43 (cl (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule symm :premises (t3.t2.a2))
% 30.71/31.13  (step t3.t2.t44 (cl (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a))))) :rule symm :premises (t3.t2.t43))
% 30.71/31.13  (step t3.t2.t45 (cl (= (tptp.inverse (tptp.inverse tptp.a)) tptp.a)) :rule symm :premises (t3.t2.a5))
% 30.71/31.13  (step t3.t2.t46 (cl (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) :rule cong :premises (t3.t2.t11 t3.t2.t45))
% 30.71/31.13  (step t3.t2.t47 (cl (= (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a))) :rule trans :premises (t3.t2.t16 t3.t2.t17 t3.t2.t18 t3.t2.t42 t3.t2.t44 t3.t2.t46))
% 30.71/31.13  (step t3.t2.t48 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (tptp.least_upper_bound (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.a)))) :rule cong :premises (t3.t2.t14 t3.t2.t47))
% 30.71/31.13  (step t3.t2.t49 (cl (= (tptp.least_upper_bound (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.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) :rule symm :premises (t3.t2.a13))
% 30.71/31.13  (step t3.t2.t50 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (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.least_upper_bound tptp.a tptp.identity)))) :rule symm :premises (t3.t2.a7))
% 30.71/31.13  (step t3.t2.t51 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule trans :premises (t3.t2.t2 t3.t2.t4 t3.t2.t48 t3.t2.t49 t3.t2.t50))
% 30.71/31.13  (step t3.t2 (cl (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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)))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a)))) (not (= tptp.identity (tptp.inverse tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule subproof :discharge (t3.t2.a0 t3.t2.a1 t3.t2.a2 t3.t2.a3 t3.t2.a4 t3.t2.a5 t3.t2.a6 t3.t2.a7 t3.t2.a8 t3.t2.a9 t3.t2.a10 t3.t2.a11 t3.t2.a12 t3.t2.a13 t3.t2.a14 t3.t2.a15 t3.t2.a16 t3.t2.a17 t3.t2.a18))
% 30.71/31.13  (step t3.t3 (cl (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule and_pos)
% 30.71/31.13  (step t3.t4 (cl (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) :rule and_pos)
% 30.71/31.13  (step t3.t5 (cl (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a))))) :rule and_pos)
% 30.71/31.13  (step t3.t6 (cl (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) :rule and_pos)
% 30.71/31.13  (step t3.t7 (cl (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule and_pos)
% 30.71/31.13  (step t3.t8 (cl (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule and_pos)
% 30.71/31.13  (step t3.t9 (cl (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) :rule and_pos)
% 30.71/31.13  (step t3.t10 (cl (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) :rule and_pos)
% 30.71/31.13  (step t3.t11 (cl (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) 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)
% 30.71/31.13  (step t3.t12 (cl (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity)))) :rule and_pos)
% 30.71/31.13  (step t3.t13 (cl (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule and_pos)
% 30.71/31.13  (step t3.t14 (cl (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule and_pos)
% 30.71/31.13  (step t3.t15 (cl (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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)
% 30.71/31.13  (step t3.t16 (cl (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a)))) :rule and_pos)
% 30.71/31.13  (step t3.t17 (cl (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.inverse tptp.identity))) :rule and_pos)
% 30.71/31.13  (step t3.t18 (cl (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule and_pos)
% 30.71/31.13  (step t3.t19 (cl (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule and_pos)
% 30.71/31.13  (step t3.t20 (cl (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity)))) :rule and_pos)
% 30.71/31.13  (step t3.t21 (cl (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule and_pos)
% 30.71/31.13  (step t3.t22 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule resolution :premises (t3.t2 t3.t3 t3.t4 t3.t5 t3.t6 t3.t7 t3.t8 t3.t9 t3.t10 t3.t11 t3.t12 t3.t13 t3.t14 t3.t15 t3.t16 t3.t17 t3.t18 t3.t19 t3.t20 t3.t21))
% 30.71/31.14  (step t3.t23 (cl (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule reordering :premises (t3.t22))
% 30.71/31.14  (step t3.t24 (cl (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule contraction :premises (t3.t23))
% 30.71/31.14  (step t3.t25 (cl (=> (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule resolution :premises (t3.t1 t3.t24))
% 30.71/31.14  (step t3.t26 (cl (=> (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule implies_neg2)
% 30.71/31.14  (step t3.t27 (cl (=> (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (=> (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule resolution :premises (t3.t25 t3.t26))
% 30.71/31.14  (step t3.t28 (cl (=> (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule contraction :premises (t3.t27))
% 30.71/31.14  (step t3.t29 (cl (not (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule implies :premises (t3.t28))
% 30.71/31.14  (step t3.t30 (cl (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a))))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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)))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a)))) (not (= tptp.identity (tptp.inverse tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity)))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule and_neg)
% 30.71/31.14  (step t3.t31 (cl (and (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a 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.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (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.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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule resolution :premises (t3.t30 t3.a16 t3.a15 t3.a13 t3.a9 t3.a17 t3.a11 t3.a1 t3.a2 t3.a4 t3.a7 t3.a18 t3.a14 t3.a3 t3.a5 t3.a0 t3.a8 t3.a6 t3.a12 t3.a10))
% 30.71/31.14  (step t3.t32 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule resolution :premises (t3.t29 t3.t31))
% 30.71/31.14  (step t3 (cl (not (= tptp.identity (tptp.inverse tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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)))))) (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.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a)))) (not (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound 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.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule subproof :discharge (t3.a0 t3.a1 t3.a2 t3.a3 t3.a4 t3.a5 t3.a6 t3.a7 t3.a8 t3.a9 t3.a10 t3.a11 t3.a12 t3.a13 t3.a14 t3.a15 t3.a16 t3.a17 t3.a18))
% 30.71/31.14  (step t4 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.inverse tptp.identity))) :rule and_pos)
% 30.71/31.14  (step t5 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) :rule and_pos)
% 30.71/31.14  (step t6 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) :rule and_pos)
% 30.71/31.14  (step t7 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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)
% 30.71/31.14  (step t8 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse 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)
% 30.71/31.14  (step t9 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a)))) :rule and_pos)
% 30.71/31.14  (step t10 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule and_pos)
% 30.71/31.14  (step t11 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity)))) :rule and_pos)
% 30.71/31.14  (step t12 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (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)
% 30.71/31.14  (step t13 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) :rule and_pos)
% 30.71/31.14  (step t14 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule and_pos)
% 30.71/31.14  (step t15 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule and_pos)
% 30.71/31.14  (step t16 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity)))) :rule and_pos)
% 30.71/31.14  (step t17 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a))))) :rule and_pos)
% 30.71/31.14  (step t18 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule and_pos)
% 30.71/31.14  (step t19 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) :rule and_pos)
% 30.71/31.14  (step t20 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule and_pos)
% 30.71/31.14  (step t21 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule and_pos)
% 30.71/31.14  (step t22 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule and_pos)
% 30.71/31.14  (step t23 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))))) :rule resolution :premises (t3 t4 t5 t6 t7 t8 t9 t10 t11 t12 t13 t14 t15 t16 t17 t18 t19 t20 t21 t22))
% 30.71/31.14  (step t24 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule reordering :premises (t23))
% 30.71/31.14  (step t25 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule contraction :premises (t24))
% 30.71/31.14  (step t26 (cl (=> (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule resolution :premises (t2 t25))
% 30.71/31.14  (step t27 (cl (=> (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule implies_neg2)
% 30.71/31.14  (step t28 (cl (=> (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (=> (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule resolution :premises (t26 t27))
% 30.71/31.14  (step t29 (cl (=> (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule contraction :premises (t28))
% 30.71/31.14  (step t30 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a)) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule implies :premises (t29))
% 30.71/31.14  (step t31 (cl (not (= tptp.identity (tptp.inverse tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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)))))) (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.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a)))) (not (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound 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.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule resolution :premises (t1 t30))
% 30.71/31.14  (step t32 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (not (= tptp.identity (tptp.inverse tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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)))))) (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.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a)))) (not (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound 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.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) :rule reordering :premises (t31))
% 30.71/31.14  (step t33 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) :rule implies_neg1)
% 30.71/31.14  (anchor :step t34)
% 30.71/31.14  (assume t34.a0 (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))))
% 30.71/31.14  (step t34.t1 (cl (or (not (forall ((Y $$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.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) :rule forall_inst :args ((:= Y tptp.identity) (:= Z tptp.a) (:= X (tptp.inverse tptp.a))))
% 30.71/31.14  (step t34.t2 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule or :premises (t34.t1))
% 30.71/31.14  (step t34.t3 (cl (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule resolution :premises (t34.t2 t34.a0))
% 30.71/31.14  (step t34 (cl (not (forall ((Y $$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.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule subproof :discharge (t34.a0))
% 30.71/31.14  (step t35 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule resolution :premises (t33 t34))
% 30.71/31.14  (step t36 (cl (=> (forall ((Y $$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.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) :rule implies_neg2)
% 30.71/31.14  (step t37 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) :rule resolution :premises (t35 t36))
% 30.71/31.14  (step t38 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) :rule contraction :premises (t37))
% 30.71/31.14  (step t39 (cl (not (forall ((Y $$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.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule implies :premises (t38))
% 30.71/31.14  (step t40 (cl (= (tptp.multiply (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule resolution :premises (t39 a14))
% 30.71/31.14  (step t41 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z))))) :rule implies_neg1)
% 30.71/31.14  (anchor :step t42)
% 30.71/31.14  (assume t42.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))))
% 30.71/31.14  (step t42.t1 (cl (or (not (forall ((X $$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.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.a)) (:= Y tptp.identity) (:= Z tptp.a)))
% 30.71/31.14  (step t42.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule or :premises (t42.t1))
% 30.71/31.14  (step t42.t3 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule resolution :premises (t42.t2 t42.a0))
% 30.71/31.14  (step t42 (cl (not (forall ((X $$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.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule subproof :discharge (t42.a0))
% 30.71/31.14  (step t43 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule resolution :premises (t41 t42))
% 30.71/31.14  (step t44 (cl (=> (forall ((X $$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.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule implies_neg2)
% 30.71/31.14  (step t45 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule resolution :premises (t43 t44))
% 30.71/31.14  (step t46 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule contraction :premises (t45))
% 30.71/31.14  (step t47 (cl (not (forall ((X $$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.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule implies :premises (t46))
% 30.71/31.14  (step t48 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.identity tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule resolution :premises (t47 a12))
% 30.71/31.14  (step t49 (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)
% 30.71/31.14  (anchor :step t50)
% 30.71/31.14  (assume t50.a0 (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))))
% 30.71/31.14  (step t50.t1 (cl (or (not (forall ((X $$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))))
% 30.71/31.14  (step t50.t2 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule or :premises (t50.t1))
% 30.71/31.14  (step t50.t3 (cl (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule resolution :premises (t50.t2 t50.a0))
% 30.71/31.14  (step t50 (cl (not (forall ((X $$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 (t50.a0))
% 30.71/31.14  (step t51 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule resolution :premises (t49 t50))
% 30.71/31.14  (step t52 (cl (=> (forall ((X $$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)
% 30.71/31.14  (step t53 (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 (t51 t52))
% 30.71/31.14  (step t54 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule contraction :premises (t53))
% 30.71/31.14  (step t55 (cl (not (forall ((X $$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 (t54))
% 30.71/31.14  (step t56 (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)
% 30.71/31.14  (anchor :step t57 :args ((X $$unsorted) (:= X X)))
% 30.71/31.14  (step t57.t1 (cl (= X X)) :rule refl)
% 30.71/31.14  (step t57.t2 (cl (= (= (tptp.multiply (tptp.inverse X) X) tptp.identity) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) :rule all_simplify)
% 30.71/31.14  (step t57 (cl (= (forall ((X $$unsorted)) (= (tptp.multiply (tptp.inverse X) X) tptp.identity)) (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))))) :rule bind)
% 30.71/31.14  (step t58 (cl (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) :rule resolution :premises (t56 t57 a1))
% 30.71/31.14  (step t59 (cl (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule resolution :premises (t55 t58))
% 30.71/31.14  (step t60 (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)
% 30.71/31.14  (anchor :step t61)
% 30.71/31.14  (assume t61.a0 (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))))
% 30.71/31.14  (step t61.t1 (cl (or (not (forall ((X $$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))))
% 30.71/31.14  (step t61.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) :rule or :premises (t61.t1))
% 30.71/31.14  (step t61.t3 (cl (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) :rule resolution :premises (t61.t2 t61.a0))
% 30.71/31.14  (step t61 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) :rule subproof :discharge (t61.a0))
% 30.71/31.14  (step t62 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) :rule resolution :premises (t60 t61))
% 30.71/31.14  (step t63 (cl (=> (forall ((X $$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)
% 30.71/31.14  (step t64 (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 (t62 t63))
% 30.71/31.14  (step t65 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) :rule contraction :premises (t64))
% 30.71/31.14  (step t66 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) :rule implies :premises (t65))
% 30.71/31.14  (step t67 (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)
% 30.71/31.14  (anchor :step t68 :args ((X $$unsorted) (:= X X)))
% 30.71/31.14  (step t68.t1 (cl (= X X)) :rule refl)
% 30.71/31.14  (step t68.t2 (cl (= (= (tptp.multiply tptp.identity X) X) (= X (tptp.multiply tptp.identity X)))) :rule all_simplify)
% 30.71/31.14  (step t68 (cl (= (forall ((X $$unsorted)) (= (tptp.multiply tptp.identity X) X)) (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))))) :rule bind)
% 30.71/31.14  (step t69 (cl (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) :rule resolution :premises (t67 t68 a0))
% 30.71/31.14  (step t70 (cl (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) :rule resolution :premises (t66 t69))
% 30.71/31.14  (step t71 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) :rule implies_neg1)
% 30.71/31.14  (anchor :step t72)
% 30.71/31.14  (assume t72.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))))
% 30.71/31.14  (step t72.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule forall_inst :args ((:= X (tptp.greatest_lower_bound tptp.a tptp.identity)) (:= Y (tptp.inverse tptp.a))))
% 30.71/31.14  (step t72.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule or :premises (t72.t1))
% 30.71/31.14  (step t72.t3 (cl (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule resolution :premises (t72.t2 t72.a0))
% 30.71/31.14  (step t72 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule subproof :discharge (t72.a0))
% 30.71/31.14  (step t73 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule resolution :premises (t71 t72))
% 30.71/31.14  (step t74 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (not (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule implies_neg2)
% 30.71/31.14  (step t75 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule resolution :premises (t73 t74))
% 30.71/31.14  (step t76 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule contraction :premises (t75))
% 30.71/31.14  (step t77 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule implies :premises (t76))
% 30.71/31.14  (step t78 (cl (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule resolution :premises (t77 a17))
% 30.71/31.14  (step t79 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) :rule implies_neg1)
% 30.71/31.14  (anchor :step t80)
% 30.71/31.14  (assume t80.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))))
% 30.71/31.14  (step t80.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.a)) (:= Y (tptp.greatest_lower_bound tptp.a tptp.identity))))
% 30.71/31.14  (step t80.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a))))) :rule or :premises (t80.t1))
% 30.71/31.14  (step t80.t3 (cl (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a))))) :rule resolution :premises (t80.t2 t80.a0))
% 30.71/31.14  (step t80 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a))))) :rule subproof :discharge (t80.a0))
% 30.71/31.14  (step t81 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a))))) :rule resolution :premises (t79 t80))
% 30.71/31.14  (step t82 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))))) :rule implies_neg2)
% 30.71/31.14  (step t83 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))))) :rule resolution :premises (t81 t82))
% 30.71/31.14  (step t84 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a)))))) :rule contraction :premises (t83))
% 30.71/31.14  (step t85 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a))))) :rule implies :premises (t84))
% 30.71/31.14  (step t86 (cl (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse (tptp.inverse tptp.a))))) :rule resolution :premises (t85 a17))
% 30.71/31.14  (step t87 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) :rule implies_neg1)
% 30.71/31.14  (anchor :step t88)
% 30.71/31.14  (assume t88.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))))
% 30.71/31.14  (step t88.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))))) :rule forall_inst :args ((:= X tptp.identity) (:= Y tptp.a)))
% 30.71/31.14  (step t88.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity)))) :rule or :premises (t88.t1))
% 30.71/31.14  (step t88.t3 (cl (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity)))) :rule resolution :premises (t88.t2 t88.a0))
% 30.71/31.14  (step t88 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity)))) :rule subproof :discharge (t88.a0))
% 30.71/31.14  (step t89 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity)))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity)))) :rule resolution :premises (t87 t88))
% 30.71/31.14  (step t90 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity)))) (not (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))))) :rule implies_neg2)
% 30.71/31.14  (step t91 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))))) :rule resolution :premises (t89 t90))
% 30.71/31.14  (step t92 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity))))) :rule contraction :premises (t91))
% 30.71/31.14  (step t93 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity)))) :rule implies :premises (t92))
% 30.71/31.14  (step t94 (cl (= (tptp.inverse (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse tptp.identity)))) :rule resolution :premises (t93 a17))
% 30.71/31.14  (step t95 (cl (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) :rule implies_neg1)
% 30.71/31.14  (anchor :step t96)
% 30.71/31.14  (assume t96.a0 (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))))
% 30.71/31.14  (step t96.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))) :rule forall_inst :args ((:= X tptp.a)))
% 30.71/31.14  (step t96.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule or :premises (t96.t1))
% 30.71/31.14  (step t96.t3 (cl (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule resolution :premises (t96.t2 t96.a0))
% 30.71/31.14  (step t96 (cl (not (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule subproof :discharge (t96.a0))
% 30.71/31.14  (step t97 (cl (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule resolution :premises (t95 t96))
% 30.71/31.14  (step t98 (cl (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))) :rule implies_neg2)
% 30.71/31.14  (step t99 (cl (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))) :rule resolution :premises (t97 t98))
% 30.71/31.14  (step t100 (cl (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))) :rule contraction :premises (t99))
% 30.71/31.14  (step t101 (cl (not (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule implies :premises (t100))
% 30.71/31.14  (step t102 (cl (not (= (forall ((X $$unsorted)) (= (tptp.inverse (tptp.inverse X)) X)) (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))))) (not (forall ((X $$unsorted)) (= (tptp.inverse (tptp.inverse X)) X))) (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) :rule equiv_pos2)
% 30.71/31.14  (anchor :step t103 :args ((X $$unsorted) (:= X X)))
% 30.71/31.14  (step t103.t1 (cl (= X X)) :rule refl)
% 30.71/31.14  (step t103.t2 (cl (= (= (tptp.inverse (tptp.inverse X)) X) (= X (tptp.inverse (tptp.inverse X))))) :rule all_simplify)
% 30.71/31.14  (step t103 (cl (= (forall ((X $$unsorted)) (= (tptp.inverse (tptp.inverse X)) X)) (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))))) :rule bind)
% 30.71/31.14  (step t104 (cl (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) :rule resolution :premises (t102 t103 a16))
% 30.71/31.14  (step t105 (cl (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule resolution :premises (t101 t104))
% 30.71/31.14  (step t106 (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)
% 30.71/31.14  (anchor :step t107)
% 30.71/31.14  (assume t107.a0 (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))))
% 30.71/31.14  (step t107.t1 (cl (or (not (forall ((X $$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)))
% 30.71/31.14  (step t107.t2 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule or :premises (t107.t1))
% 30.71/31.14  (step t107.t3 (cl (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule resolution :premises (t107.t2 t107.a0))
% 30.71/31.14  (step t107 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule subproof :discharge (t107.a0))
% 30.71/31.14  (step t108 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule resolution :premises (t106 t107))
% 30.71/31.14  (step t109 (cl (=> (forall ((X $$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)
% 30.71/31.14  (step t110 (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 (t108 t109))
% 30.71/31.14  (step t111 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule contraction :premises (t110))
% 30.71/31.14  (step t112 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule implies :premises (t111))
% 30.71/31.14  (step t113 (cl (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule resolution :premises (t112 t58))
% 30.71/31.14  (step t114 (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)
% 30.71/31.14  (anchor :step t115)
% 30.71/31.14  (assume t115.a0 (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))))
% 30.71/31.14  (step t115.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)))) :rule forall_inst :args ((:= X tptp.a)))
% 30.71/31.14  (step t115.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) :rule or :premises (t115.t1))
% 30.71/31.14  (step t115.t3 (cl (= tptp.a (tptp.multiply tptp.identity tptp.a))) :rule resolution :premises (t115.t2 t115.a0))
% 30.71/31.14  (step t115 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) :rule subproof :discharge (t115.a0))
% 30.71/31.14  (step t116 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) :rule resolution :premises (t114 t115))
% 30.71/31.14  (step t117 (cl (=> (forall ((X $$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)
% 30.71/31.14  (step t118 (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 (t116 t117))
% 30.71/31.14  (step t119 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.a (tptp.multiply tptp.identity tptp.a)))) :rule contraction :premises (t118))
% 30.71/31.14  (step t120 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) :rule implies :premises (t119))
% 30.71/31.14  (step t121 (cl (= tptp.a (tptp.multiply tptp.identity tptp.a))) :rule resolution :premises (t120 t69))
% 30.71/31.14  (step t122 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) :rule implies_neg1)
% 30.71/31.14  (anchor :step t123)
% 30.71/31.14  (assume t123.a0 (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))))
% 30.71/31.14  (step t123.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule forall_inst :args ((:= X (tptp.greatest_lower_bound tptp.a tptp.identity))))
% 30.71/31.14  (step t123.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule or :premises (t123.t1))
% 30.71/31.14  (step t123.t3 (cl (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule resolution :premises (t123.t2 t123.a0))
% 30.71/31.14  (step t123 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule subproof :discharge (t123.a0))
% 30.71/31.14  (step t124 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule resolution :premises (t122 t123))
% 30.71/31.14  (step t125 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule implies_neg2)
% 30.71/31.14  (step t126 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule resolution :premises (t124 t125))
% 30.71/31.14  (step t127 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule contraction :premises (t126))
% 30.71/31.14  (step t128 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule implies :premises (t127))
% 30.71/31.14  (step t129 (cl (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule resolution :premises (t128 t69))
% 30.71/31.14  (step t130 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) :rule implies_neg1)
% 30.71/31.14  (anchor :step t131)
% 30.71/31.14  (assume t131.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))))
% 30.71/31.14  (step t131.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))))) :rule forall_inst :args ((:= X tptp.identity) (:= Y (tptp.greatest_lower_bound tptp.a tptp.identity))))
% 30.71/31.14  (step t131.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity)))) :rule or :premises (t131.t1))
% 30.71/31.14  (step t131.t3 (cl (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity)))) :rule resolution :premises (t131.t2 t131.a0))
% 30.71/31.14  (step t131 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity)))) :rule subproof :discharge (t131.a0))
% 30.71/31.14  (step t132 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity)))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity)))) :rule resolution :premises (t130 t131))
% 30.71/31.14  (step t133 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity)))) (not (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))))) :rule implies_neg2)
% 30.71/31.14  (step t134 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))))) :rule resolution :premises (t132 t133))
% 30.71/31.14  (step t135 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity))))) :rule contraction :premises (t134))
% 30.71/31.14  (step t136 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity)))) :rule implies :premises (t135))
% 30.71/31.14  (step t137 (cl (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.inverse tptp.identity)))) :rule resolution :premises (t136 a17))
% 30.71/31.14  (step t138 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) :rule implies_neg1)
% 30.71/31.14  (anchor :step t139)
% 30.71/31.14  (assume t139.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))))
% 30.71/31.14  (step t139.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) :rule forall_inst :args ((:= X (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (:= Y (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))
% 30.71/31.14  (step t139.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule or :premises (t139.t1))
% 30.71/31.14  (step t139.t3 (cl (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule resolution :premises (t139.t2 t139.a0))
% 30.71/31.14  (step t139 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule subproof :discharge (t139.a0))
% 30.71/31.14  (step t140 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule resolution :premises (t138 t139))
% 30.71/31.14  (step t141 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (not (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) :rule implies_neg2)
% 30.71/31.14  (step t142 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) :rule resolution :premises (t140 t141))
% 30.71/31.14  (step t143 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) :rule contraction :premises (t142))
% 30.71/31.14  (step t144 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule implies :premises (t143))
% 30.71/31.14  (step t145 (cl (= (tptp.least_upper_bound (tptp.multiply 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)))) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule resolution :premises (t144 a4))
% 30.71/31.14  (step t146 (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.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) :rule implies_neg1)
% 30.71/31.14  (anchor :step t147)
% 30.71/31.14  (assume t147.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))))
% 30.71/31.14  (step t147.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.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))))) :rule forall_inst :args ((:= X (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) (:= Y (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))))
% 30.71/31.14  (step t147.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.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a)))) :rule or :premises (t147.t1))
% 30.71/31.14  (step t147.t3 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a)))) :rule resolution :premises (t147.t2 t147.a0))
% 30.71/31.14  (step t147 (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.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a)))) :rule subproof :discharge (t147.a0))
% 30.71/31.14  (step t148 (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.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a)))) :rule resolution :premises (t146 t147))
% 30.71/31.14  (step t149 (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.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))))) :rule implies_neg2)
% 30.71/31.14  (step t150 (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.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.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.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))))) :rule resolution :premises (t148 t149))
% 30.71/31.14  (step t151 (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.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a))))) :rule contraction :premises (t150))
% 30.71/31.14  (step t152 (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.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a)))) :rule implies :premises (t151))
% 30.71/31.14  (step t153 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (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.a)))) :rule resolution :premises (t152 a4))
% 30.71/31.14  (step t154 (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)
% 30.71/31.14  (anchor :step t155)
% 30.71/31.14  (assume t155.a0 (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))))
% 30.71/31.14  (step t155.t1 (cl (or (not (forall ((X $$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)))))
% 30.71/31.14  (step t155.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule or :premises (t155.t1))
% 30.71/31.14  (step t155.t3 (cl (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule resolution :premises (t155.t2 t155.a0))
% 30.71/31.14  (step t155 (cl (not (forall ((X $$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 (t155.a0))
% 30.71/31.14  (step t156 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule resolution :premises (t154 t155))
% 30.71/31.14  (step t157 (cl (=> (forall ((X $$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)
% 30.71/31.14  (step t158 (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 (t156 t157))
% 30.71/31.14  (step t159 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule contraction :premises (t158))
% 30.71/31.14  (step t160 (cl (not (forall ((X $$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 (t159))
% 30.71/31.14  (step t161 (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 (t160 t69))
% 30.71/31.14  (step t162 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (forall ((Y $$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)
% 30.71/31.14  (anchor :step t163)
% 30.71/31.14  (assume t163.a0 (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))))
% 30.71/31.14  (step t163.t1 (cl (or (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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 forall_inst :args ((:= Y tptp.a) (:= Z tptp.identity) (:= X (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))
% 30.71/31.14  (step t163.t2 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule or :premises (t163.t1))
% 30.71/31.14  (step t163.t3 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule resolution :premises (t163.t2 t163.a0))
% 30.71/31.14  (step t163 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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 subproof :discharge (t163.a0))
% 30.71/31.14  (step t164 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule resolution :premises (t162 t163))
% 30.71/31.14  (step t165 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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)))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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 implies_neg2)
% 30.71/31.14  (step t166 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)))))) (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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 resolution :premises (t164 t165))
% 30.71/31.14  (step t167 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))))))) :rule contraction :premises (t166))
% 30.71/31.14  (step t168 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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 implies :premises (t167))
% 30.71/31.14  (step t169 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.multiply 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 resolution :premises (t168 a13))
% 30.71/31.14  (step t170 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (forall ((X $$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)
% 30.71/31.14  (anchor :step t171)
% 30.71/31.14  (assume t171.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))))
% 30.71/31.14  (step t171.t1 (cl (or (not (forall ((X $$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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))))) :rule forall_inst :args ((:= X (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity))) (:= Y tptp.a) (:= Z tptp.identity)))
% 30.71/31.14  (step t171.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) :rule or :premises (t171.t1))
% 30.71/31.14  (step t171.t3 (cl (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) :rule resolution :premises (t171.t2 t171.a0))
% 30.71/31.14  (step t171 (cl (not (forall ((X $$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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) :rule subproof :discharge (t171.a0))
% 30.71/31.14  (step t172 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) :rule resolution :premises (t170 t171))
% 30.71/31.14  (step t173 (cl (=> (forall ((X $$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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))))) :rule implies_neg2)
% 30.71/31.14  (step t174 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) (=> (forall ((X $$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.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))))) :rule resolution :premises (t172 t173))
% 30.71/31.14  (step t175 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity))))) :rule contraction :premises (t174))
% 30.71/31.14  (step t176 (cl (not (forall ((X $$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.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) :rule implies :premises (t175))
% 30.71/31.14  (step t177 (cl (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.identity)))) :rule resolution :premises (t176 a11))
% 30.71/31.14  (step t178 (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)
% 30.71/31.14  (anchor :step t179)
% 30.71/31.14  (assume t179.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))))
% 30.71/31.14  (step t179.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)))
% 30.71/31.14  (step t179.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 (t179.t1))
% 30.71/31.14  (step t179.t3 (cl (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) :rule resolution :premises (t179.t2 t179.a0))
% 30.71/31.14  (step t179 (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 (t179.a0))
% 30.71/31.14  (step t180 (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 (t178 t179))
% 30.71/31.14  (step t181 (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)
% 30.71/31.14  (step t182 (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 (t180 t181))
% 30.71/31.14  (step t183 (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 (t182))
% 30.71/31.14  (step t184 (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 (t183))
% 30.71/31.14  (step t185 (cl (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) :rule resolution :premises (t184 a3))
% 30.71/31.14  (step t186 (cl (= tptp.identity (tptp.inverse tptp.identity))) :rule symm :premises (a15))
% 30.71/31.14  (step t187 (cl) :rule resolution :premises (t32 t40 t48 t59 t70 t78 t86 t94 t105 t113 t121 t129 t137 t145 t153 t161 t169 t177 t185 a18 t186))
% 30.71/31.14  
% 30.71/31.14  % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.LGXdLJ4SQZ/cvc5---1.0.5_20700.smt2
% 30.71/31.14  % cvc5---1.0.5 exiting
% 30.71/31.14  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------