%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : GRP172-2 : TPTP v8.2.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : do_cvc5 %s %d

% Computer : n022.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 16:53:32 EDT 2024

% Result   : Unsatisfiable 0.38s 0.57s
% Output   : Proof 0.40s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : GRP172-2 : TPTP v8.2.0. Bugfixed v1.2.1.
% 0.14/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n022.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Sun May 26 18:51:24 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.20/0.50  %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.51  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.38/0.57  % SZS status Unsatisfiable for /export/starexec/sandbox/tmp/tmp.yHWSQS77WP/cvc5---1.0.5_27924.smt2
% 0.38/0.57  % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.yHWSQS77WP/cvc5---1.0.5_27924.smt2
% 0.40/0.59  (assume a0 (forall ((X $$unsorted)) (= (tptp.multiply tptp.identity X) X)))
% 0.40/0.59  (assume a1 (forall ((X $$unsorted)) (= (tptp.multiply (tptp.inverse X) X) tptp.identity)))
% 0.40/0.59  (assume a2 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 0.40/0.59  (assume a3 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))))
% 0.40/0.59  (assume a4 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))))
% 0.40/0.59  (assume a5 (forall ((X $$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))))
% 0.40/0.59  (assume a6 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))))
% 0.40/0.59  (assume a7 (forall ((X $$unsorted)) (= (tptp.least_upper_bound X X) X)))
% 0.40/0.59  (assume a8 (forall ((X $$unsorted)) (= (tptp.greatest_lower_bound X X) X)))
% 0.40/0.59  (assume a9 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)) X)))
% 0.40/0.59  (assume a10 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)) X)))
% 0.40/0.59  (assume a11 (forall ((X $$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)))))
% 0.40/0.59  (assume a12 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))))
% 0.40/0.59  (assume a13 (forall ((Y $$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)))))
% 0.40/0.59  (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)))))
% 0.40/0.59  (assume a15 (= (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity))
% 0.40/0.59  (assume a16 (= (tptp.greatest_lower_bound tptp.identity tptp.b) tptp.identity))
% 0.40/0.59  (assume a17 (not (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.multiply tptp.a tptp.b))))
% 0.40/0.59  (step t1 (cl (not (= (or (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b))) (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) (not (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) (or (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b))) (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) (not (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))))) (not (or (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b))) (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) (not (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity))))) (or (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b))) (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) (not (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity))))) :rule equiv_pos2)
% 0.40/0.59  (step t2 (cl (= (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) :rule refl)
% 0.40/0.59  (step t3 (cl (= (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b))))) :rule refl)
% 0.40/0.59  (step t4 (cl (= (= (= (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) true) (= (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))))) :rule equiv_simplify)
% 0.40/0.59  (step t5 (cl (not (= (= (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) true)) (= (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) :rule equiv1 :premises (t4))
% 0.40/0.59  (step t6 (cl (= (= (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))) (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))))))) :rule all_simplify)
% 0.40/0.59  (step t7 (cl (= (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))) (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) :rule refl)
% 0.40/0.59  (step t8 (cl (= (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) :rule all_simplify)
% 0.40/0.59  (step t9 (cl (= (= (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))) (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))))) (= (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))) (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))))) :rule cong :premises (t7 t8))
% 0.40/0.59  (step t10 (cl (= (= (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))) (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) true)) :rule all_simplify)
% 0.40/0.59  (step t11 (cl (= (= (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))) (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))))) true)) :rule trans :premises (t9 t10))
% 0.40/0.59  (step t12 (cl (= (= (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) true)) :rule trans :premises (t6 t11))
% 0.40/0.59  (step t13 (cl (= (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) :rule resolution :premises (t5 t12))
% 0.40/0.59  (step t14 (cl (= (not (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule refl)
% 0.40/0.59  (step t15 (cl (= (not (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))))) :rule refl)
% 0.40/0.59  (step t16 (cl (= (not (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (not (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))))) :rule refl)
% 0.40/0.59  (step t17 (cl (= (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))))) :rule refl)
% 0.40/0.59  (step t18 (cl (= (not (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) (not (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))))) :rule refl)
% 0.40/0.59  (step t19 (cl (= (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule refl)
% 0.40/0.59  (step t20 (cl (= (not (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) (not (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))))) :rule refl)
% 0.40/0.59  (step t21 (cl (= (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))))) :rule refl)
% 0.40/0.59  (step t22 (cl (= (not (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b))))) :rule refl)
% 0.40/0.59  (step t23 (cl (= (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity))))) :rule refl)
% 0.40/0.59  (step t24 (cl (= (or (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b))) (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) (not (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) (or (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b))) (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) (not (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))))) :rule cong :premises (t2 t3 t13 t14 t15 t16 t17 t18 t19 t20 t21 t22 t23))
% 0.40/0.59  (step t25 (cl (and (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b))) (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) (not (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b)))) :rule and_neg)
% 0.40/0.59  (step t26 (cl (=> (and (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) (and (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= tptp.b (tptp.multiply tptp.identity tptp.b)))) :rule implies_neg1)
% 0.40/0.59  (anchor :step t27)
% 0.40/0.59  (assume t27.a0 (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))
% 0.40/0.59  (assume t27.a1 (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)))
% 0.40/0.59  (assume t27.a2 (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))))
% 0.40/0.59  (assume t27.a3 (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))
% 0.40/0.59  (assume t27.a4 (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)))
% 0.40/0.59  (assume t27.a5 (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)))
% 0.40/0.59  (assume t27.a6 (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))
% 0.40/0.59  (assume t27.a7 (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)))
% 0.40/0.59  (assume t27.a8 (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))
% 0.40/0.59  (assume t27.a9 (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))))
% 0.40/0.59  (assume t27.a10 (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))))
% 0.40/0.59  (assume t27.a11 (= tptp.b (tptp.multiply tptp.identity tptp.b)))
% 0.40/0.59  (step t27.t1 (cl (=> (and (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) (and (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) :rule implies_neg1)
% 0.40/0.59  (anchor :step t27.t2)
% 0.40/0.59  (assume t27.t2.a0 (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))))
% 0.40/0.59  (assume t27.t2.a1 (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)))
% 0.40/0.59  (assume t27.t2.a2 (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))
% 0.40/0.59  (assume t27.t2.a3 (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))))
% 0.40/0.59  (assume t27.t2.a4 (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))
% 0.40/0.59  (assume t27.t2.a5 (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))
% 0.40/0.59  (assume t27.t2.a6 (= tptp.b (tptp.multiply tptp.identity tptp.b)))
% 0.40/0.59  (assume t27.t2.a7 (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))))
% 0.40/0.59  (assume t27.t2.a8 (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)))
% 0.40/0.59  (assume t27.t2.a9 (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)))
% 0.40/0.59  (assume t27.t2.a10 (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)))
% 0.40/0.59  (assume t27.t2.a11 (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))
% 0.40/0.59  (step t27.t2.t1 (cl (= (= (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)) false) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity))))) :rule equiv_simplify)
% 0.40/0.59  (step t27.t2.t2 (cl (not (= (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)) false)) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) :rule equiv1 :premises (t27.t2.t1))
% 0.40/0.59  (step t27.t2.t3 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b))) :rule symm :premises (t27.t2.a3))
% 0.40/0.59  (step t27.t2.t4 (cl (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.a)) :rule symm :premises (t27.t2.a2))
% 0.40/0.59  (step t27.t2.t5 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.b tptp.b)))) :rule cong :premises (t27.t2.t4 t27.t2.a1))
% 0.40/0.59  (step t27.t2.t6 (cl (= tptp.a tptp.a)) :rule refl)
% 0.40/0.59  (step t27.t2.t7 (cl (= (tptp.greatest_lower_bound tptp.b tptp.b) tptp.b)) :rule symm :premises (t27.t2.a1))
% 0.40/0.59  (step t27.t2.t8 (cl (= (tptp.multiply tptp.a (tptp.greatest_lower_bound tptp.b tptp.b)) (tptp.multiply tptp.a tptp.b))) :rule cong :premises (t27.t2.t6 t27.t2.t7))
% 0.40/0.59  (step t27.t2.t9 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) (tptp.multiply tptp.a tptp.b))) :rule trans :premises (t27.t2.t3 t27.t2.t5 t27.t2.t8))
% 0.40/0.59  (step t27.t2.t10 (cl (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) :rule symm :premises (t27.t2.t9))
% 0.40/0.59  (step t27.t2.t11 (cl (= (tptp.greatest_lower_bound tptp.identity tptp.a) tptp.identity)) :rule symm :premises (t27.t2.a5))
% 0.40/0.59  (step t27.t2.t12 (cl (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) :rule symm :premises (t27.t2.t11))
% 0.40/0.59  (step t27.t2.t13 (cl (= (tptp.greatest_lower_bound tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.a))) :rule symm :premises (t27.t2.a4))
% 0.40/0.59  (step t27.t2.t14 (cl (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) :rule symm :premises (t27.t2.t13))
% 0.40/0.59  (step t27.t2.t15 (cl (= tptp.identity (tptp.greatest_lower_bound tptp.a tptp.identity))) :rule trans :premises (t27.t2.t12 t27.t2.t14))
% 0.40/0.59  (step t27.t2.t16 (cl (= tptp.b tptp.b)) :rule refl)
% 0.40/0.59  (step t27.t2.t17 (cl (= (tptp.multiply tptp.identity tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) :rule cong :premises (t27.t2.t15 t27.t2.t16))
% 0.40/0.59  (step t27.t2.t18 (cl (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) (tptp.multiply tptp.identity tptp.b))) :rule symm :premises (t27.t2.t17))
% 0.40/0.59  (step t27.t2.t19 (cl (= (tptp.multiply tptp.identity tptp.b) tptp.b)) :rule symm :premises (t27.t2.a6))
% 0.40/0.59  (step t27.t2.t20 (cl (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.b)) :rule trans :premises (t27.t2.t18 t27.t2.t19))
% 0.40/0.59  (step t27.t2.t21 (cl (= (tptp.greatest_lower_bound tptp.identity tptp.b) tptp.identity)) :rule symm :premises (t27.t2.a9))
% 0.40/0.59  (step t27.t2.t22 (cl (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b))) :rule symm :premises (t27.t2.t21))
% 0.40/0.59  (step t27.t2.t23 (cl (= (tptp.greatest_lower_bound tptp.b tptp.identity) (tptp.greatest_lower_bound tptp.identity tptp.b))) :rule symm :premises (t27.t2.a8))
% 0.40/0.59  (step t27.t2.t24 (cl (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) :rule symm :premises (t27.t2.t23))
% 0.40/0.59  (step t27.t2.t25 (cl (= tptp.identity (tptp.greatest_lower_bound tptp.b tptp.identity))) :rule trans :premises (t27.t2.t22 t27.t2.t24))
% 0.40/0.59  (step t27.t2.t26 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity) (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) :rule cong :premises (t27.t2.t20 t27.t2.t25))
% 0.40/0.59  (step t27.t2.t27 (cl (= (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)) tptp.b)) :rule symm :premises (t27.t2.a7))
% 0.40/0.59  (step t27.t2.t28 (cl (= tptp.b (tptp.multiply tptp.identity tptp.b))) :rule symm :premises (t27.t2.t19))
% 0.40/0.59  (step t27.t2.t29 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) :rule trans :premises (t27.t2.t26 t27.t2.t27 t27.t2.t28 t27.t2.t17))
% 0.40/0.59  (step t27.t2.t30 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) :rule cong :premises (t27.t2.t10 t27.t2.t29))
% 0.40/0.59  (step t27.t2.t31 (cl (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) :rule refl)
% 0.40/0.59  (step t27.t2.t32 (cl (= (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) :rule cong :premises (t27.t2.t9 t27.t2.t31))
% 0.40/0.59  (step t27.t2.t33 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.multiply tptp.a tptp.b))) :rule trans :premises (t27.t2.t30 t27.t2.t32 t27.t2.t3 t27.t2.t5 t27.t2.t8))
% 0.40/0.59  (step t27.t2.t34 (cl (= (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) :rule cong :premises (t27.t2.t9 t27.t2.a11))
% 0.40/0.59  (step t27.t2.t35 (cl (= (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a tptp.b))) :rule refl)
% 0.40/0.59  (step t27.t2.t36 (cl (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) tptp.identity)) :rule symm :premises (t27.t2.a11))
% 0.40/0.59  (step t27.t2.t37 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) :rule cong :premises (t27.t2.t35 t27.t2.t36))
% 0.40/0.59  (step t27.t2.t38 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) :rule symm :premises (t27.t2.a10))
% 0.40/0.59  (step t27.t2.t39 (cl (= (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) :rule trans :premises (t27.t2.t34 t27.t2.t37 t27.t2.t38))
% 0.40/0.59  (step t27.t2.t40 (cl (= (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)) (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) :rule cong :premises (t27.t2.t33 t27.t2.t39))
% 0.40/0.59  (step t27.t2.t41 (cl (= (= (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))) false) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))))) :rule equiv_simplify)
% 0.40/0.59  (step t27.t2.t42 (cl (= (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))) false) (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))))) :rule equiv2 :premises (t27.t2.t41))
% 0.40/0.59  (step t27.t2.t43 (cl (not (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))))) (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) :rule not_not)
% 0.40/0.59  (step t27.t2.t44 (cl (= (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))) false) (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) :rule resolution :premises (t27.t2.t42 t27.t2.t43))
% 0.40/0.59  (step t27.t2.t45 (cl (= (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))) false)) :rule resolution :premises (t27.t2.t44 t27.t2.a0))
% 0.40/0.59  (step t27.t2.t46 (cl (= (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)) false)) :rule trans :premises (t27.t2.t40 t27.t2.t45))
% 0.40/0.59  (step t27.t2.t47 (cl (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) :rule resolution :premises (t27.t2.t2 t27.t2.t46))
% 0.40/0.59  (step t27.t2 (cl (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) (not (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b))) (not (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) :rule subproof :discharge (t27.t2.a0 t27.t2.a1 t27.t2.a2 t27.t2.a3 t27.t2.a4 t27.t2.a5 t27.t2.a6 t27.t2.a7 t27.t2.a8 t27.t2.a9 t27.t2.a10 t27.t2.a11))
% 0.40/0.59  (step t27.t3 (cl (not (and (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) :rule and_pos)
% 0.40/0.59  (step t27.t4 (cl (not (and (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) :rule and_pos)
% 0.40/0.59  (step t27.t5 (cl (not (and (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule and_pos)
% 0.40/0.59  (step t27.t6 (cl (not (and (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) :rule and_pos)
% 0.40/0.59  (step t27.t7 (cl (not (and (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) :rule and_pos)
% 0.40/0.59  (step t27.t8 (cl (not (and (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) :rule and_pos)
% 0.40/0.59  (step t27.t9 (cl (not (and (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (= tptp.b (tptp.multiply tptp.identity tptp.b))) :rule and_pos)
% 0.40/0.59  (step t27.t10 (cl (not (and (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) :rule and_pos)
% 0.40/0.59  (step t27.t11 (cl (not (and (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) :rule and_pos)
% 0.40/0.59  (step t27.t12 (cl (not (and (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b))) :rule and_pos)
% 0.40/0.59  (step t27.t13 (cl (not (and (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) :rule and_pos)
% 0.40/0.59  (step t27.t14 (cl (not (and (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) :rule and_pos)
% 0.40/0.59  (step t27.t15 (cl (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity))) (not (and (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (and (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (and (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (and (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (and (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (and (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (and (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (and (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (and (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (and (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (and (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (and (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))))) :rule resolution :premises (t27.t2 t27.t3 t27.t4 t27.t5 t27.t6 t27.t7 t27.t8 t27.t9 t27.t10 t27.t11 t27.t12 t27.t13 t27.t14))
% 0.40/0.59  (step t27.t16 (cl (not (and (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (and (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (and (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (and (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (and (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (and (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (and (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (and (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (and (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (and (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (and (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (and (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) :rule reordering :premises (t27.t15))
% 0.40/0.59  (step t27.t17 (cl (not (and (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) :rule contraction :premises (t27.t16))
% 0.40/0.59  (step t27.t18 (cl (=> (and (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) :rule resolution :premises (t27.t1 t27.t17))
% 0.40/0.59  (step t27.t19 (cl (=> (and (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) (not (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity))))) :rule implies_neg2)
% 0.40/0.59  (step t27.t20 (cl (=> (and (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) (=> (and (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity))))) :rule resolution :premises (t27.t18 t27.t19))
% 0.40/0.59  (step t27.t21 (cl (=> (and (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity))))) :rule contraction :premises (t27.t20))
% 0.40/0.59  (step t27.t22 (cl (not (and (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) :rule implies :premises (t27.t21))
% 0.40/0.59  (step t27.t23 (cl (and (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) (not (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b))) (not (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) :rule and_neg)
% 0.40/0.59  (step t27.t24 (cl (and (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) :rule resolution :premises (t27.t23 t27.a2 t27.a7 t27.a8 t27.a10 t27.a3 t27.a0 t27.a11 t27.a9 t27.a4 t27.a1 t27.a5 t27.a6))
% 0.40/0.59  (step t27.t25 (cl (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) :rule resolution :premises (t27.t22 t27.t24))
% 0.40/0.59  (step t27 (cl (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b))) (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) (not (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) :rule subproof :discharge (t27.a0 t27.a1 t27.a2 t27.a3 t27.a4 t27.a5 t27.a6 t27.a7 t27.a8 t27.a9 t27.a10 t27.a11))
% 0.40/0.59  (step t28 (cl (not (and (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= tptp.b (tptp.multiply tptp.identity tptp.b)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) :rule and_pos)
% 0.40/0.59  (step t29 (cl (not (and (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= tptp.b (tptp.multiply tptp.identity tptp.b)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b))) :rule and_pos)
% 0.40/0.59  (step t30 (cl (not (and (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= tptp.b (tptp.multiply tptp.identity tptp.b)))) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) :rule and_pos)
% 0.40/0.59  (step t31 (cl (not (and (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= tptp.b (tptp.multiply tptp.identity tptp.b)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) :rule and_pos)
% 0.40/0.59  (step t32 (cl (not (and (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= tptp.b (tptp.multiply tptp.identity tptp.b)))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) :rule and_pos)
% 0.40/0.59  (step t33 (cl (not (and (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= tptp.b (tptp.multiply tptp.identity tptp.b)))) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) :rule and_pos)
% 0.40/0.59  (step t34 (cl (not (and (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= tptp.b (tptp.multiply tptp.identity tptp.b)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) :rule and_pos)
% 0.40/0.59  (step t35 (cl (not (and (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= tptp.b (tptp.multiply tptp.identity tptp.b)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) :rule and_pos)
% 0.40/0.59  (step t36 (cl (not (and (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= tptp.b (tptp.multiply tptp.identity tptp.b)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule and_pos)
% 0.40/0.59  (step t37 (cl (not (and (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= tptp.b (tptp.multiply tptp.identity tptp.b)))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) :rule and_pos)
% 0.40/0.59  (step t38 (cl (not (and (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= tptp.b (tptp.multiply tptp.identity tptp.b)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) :rule and_pos)
% 0.40/0.59  (step t39 (cl (not (and (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= tptp.b (tptp.multiply tptp.identity tptp.b)))) (= tptp.b (tptp.multiply tptp.identity tptp.b))) :rule and_pos)
% 0.40/0.59  (step t40 (cl (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity))) (not (and (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= tptp.b (tptp.multiply tptp.identity tptp.b)))) (not (and (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= tptp.b (tptp.multiply tptp.identity tptp.b)))) (not (and (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= tptp.b (tptp.multiply tptp.identity tptp.b)))) (not (and (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= tptp.b (tptp.multiply tptp.identity tptp.b)))) (not (and (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= tptp.b (tptp.multiply tptp.identity tptp.b)))) (not (and (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= tptp.b (tptp.multiply tptp.identity tptp.b)))) (not (and (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= tptp.b (tptp.multiply tptp.identity tptp.b)))) (not (and (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= tptp.b (tptp.multiply tptp.identity tptp.b)))) (not (and (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= tptp.b (tptp.multiply tptp.identity tptp.b)))) (not (and (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= tptp.b (tptp.multiply tptp.identity tptp.b)))) (not (and (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= tptp.b (tptp.multiply tptp.identity tptp.b)))) (not (and (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= tptp.b (tptp.multiply tptp.identity tptp.b))))) :rule resolution :premises (t27 t28 t29 t30 t31 t32 t33 t34 t35 t36 t37 t38 t39))
% 0.40/0.59  (step t41 (cl (not (and (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= tptp.b (tptp.multiply tptp.identity tptp.b)))) (not (and (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= tptp.b (tptp.multiply tptp.identity tptp.b)))) (not (and (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= tptp.b (tptp.multiply tptp.identity tptp.b)))) (not (and (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= tptp.b (tptp.multiply tptp.identity tptp.b)))) (not (and (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= tptp.b (tptp.multiply tptp.identity tptp.b)))) (not (and (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= tptp.b (tptp.multiply tptp.identity tptp.b)))) (not (and (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= tptp.b (tptp.multiply tptp.identity tptp.b)))) (not (and (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= tptp.b (tptp.multiply tptp.identity tptp.b)))) (not (and (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= tptp.b (tptp.multiply tptp.identity tptp.b)))) (not (and (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= tptp.b (tptp.multiply tptp.identity tptp.b)))) (not (and (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= tptp.b (tptp.multiply tptp.identity tptp.b)))) (not (and (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= tptp.b (tptp.multiply tptp.identity tptp.b)))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) :rule reordering :premises (t40))
% 0.40/0.59  (step t42 (cl (not (and (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= tptp.b (tptp.multiply tptp.identity tptp.b)))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) :rule contraction :premises (t41))
% 0.40/0.59  (step t43 (cl (=> (and (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) :rule resolution :premises (t26 t42))
% 0.40/0.59  (step t44 (cl (=> (and (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) (not (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity))))) :rule implies_neg2)
% 0.40/0.59  (step t45 (cl (=> (and (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) (=> (and (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity))))) :rule resolution :premises (t43 t44))
% 0.40/0.59  (step t46 (cl (=> (and (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity))))) :rule contraction :premises (t45))
% 0.40/0.59  (step t47 (cl (not (and (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)) (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b)) (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))) (= tptp.b (tptp.multiply tptp.identity tptp.b)))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) :rule implies :premises (t46))
% 0.40/0.59  (step t48 (cl (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b))) (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) (not (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) :rule resolution :premises (t25 t47))
% 0.40/0.59  (step t49 (cl (or (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b))) (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) (not (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) (not (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) :rule or_neg)
% 0.40/0.59  (step t50 (cl (or (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b))) (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) (not (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) (not (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b))))) :rule or_neg)
% 0.40/0.59  (step t51 (cl (or (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b))) (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) (not (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) (not (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))))) :rule or_neg)
% 0.40/0.59  (step t52 (cl (or (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b))) (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) (not (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) (not (not (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule or_neg)
% 0.40/0.59  (step t53 (cl (or (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b))) (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) (not (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) (not (not (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))))) :rule or_neg)
% 0.40/0.59  (step t54 (cl (or (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b))) (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) (not (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) (not (not (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))))) :rule or_neg)
% 0.40/0.59  (step t55 (cl (or (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b))) (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) (not (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) (not (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))))) :rule or_neg)
% 0.40/0.59  (step t56 (cl (or (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b))) (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) (not (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) (not (not (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))))) :rule or_neg)
% 0.40/0.59  (step t57 (cl (or (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b))) (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) (not (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) (not (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))))) :rule or_neg)
% 0.40/0.59  (step t58 (cl (or (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b))) (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) (not (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) (not (not (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))))) :rule or_neg)
% 0.40/0.59  (step t59 (cl (or (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b))) (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) (not (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) (not (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))))) :rule or_neg)
% 0.40/0.59  (step t60 (cl (or (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b))) (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) (not (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) (not (not (= tptp.b (tptp.multiply tptp.identity tptp.b))))) :rule or_neg)
% 0.40/0.59  (step t61 (cl (or (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b))) (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) (not (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) (not (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity))))) :rule or_neg)
% 0.40/0.59  (step t62 (cl (or (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b))) (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) (not (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) (or (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b))) (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) (not (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) (or (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b))) (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) (not (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) (or (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b))) (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) (not (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) (or (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b))) (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) (not (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) (or (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b))) (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) (not (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) (or (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b))) (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) (not (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) (or (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b))) (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) (not (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) (or (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b))) (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) (not (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) (or (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b))) (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) (not (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) (or (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b))) (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) (not (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) (or (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b))) (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) (not (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) (or (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b))) (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) (not (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity))))) :rule resolution :premises (t48 t49 t50 t51 t52 t53 t54 t55 t56 t57 t58 t59 t60 t61))
% 0.40/0.60  (step t63 (cl (or (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b))) (not (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) (not (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity))))) :rule contraction :premises (t62))
% 0.40/0.60  (step t64 (cl (or (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b))) (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) (not (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity))))) :rule resolution :premises (t1 t24 t63))
% 0.40/0.60  (step t65 (cl (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b))) (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) (not (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) :rule or :premises (t64))
% 0.40/0.60  (step t66 (cl (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) (not (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) :rule reordering :premises (t65))
% 0.40/0.60  (step t67 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))) (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z)))) :rule implies_neg1)
% 0.40/0.60  (anchor :step t68)
% 0.40/0.60  (assume t68.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))))
% 0.40/0.60  (step t68.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) :rule forall_inst :args ((:= X (tptp.multiply tptp.a tptp.b)) (:= Y (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) (:= Z tptp.identity)))
% 0.40/0.60  (step t68.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity))) :rule or :premises (t68.t1))
% 0.40/0.60  (step t68.t3 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity))) :rule resolution :premises (t68.t2 t68.a0))
% 0.40/0.60  (step t68 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity))) :rule subproof :discharge (t68.a0))
% 0.40/0.60  (step t69 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))) (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity))) :rule resolution :premises (t67 t68))
% 0.40/0.60  (step t70 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))) (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) :rule implies_neg2)
% 0.40/0.60  (step t71 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))) (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))) (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) :rule resolution :premises (t69 t70))
% 0.40/0.60  (step t72 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))) (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity)))) :rule contraction :premises (t71))
% 0.40/0.60  (step t73 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity))) :rule implies :premises (t72))
% 0.40/0.60  (step t74 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)) tptp.identity))) :rule resolution :premises (t73 a6))
% 0.40/0.60  (step t75 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.b (tptp.multiply tptp.identity tptp.b))) (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) :rule implies_neg1)
% 0.40/0.60  (anchor :step t76)
% 0.40/0.60  (assume t76.a0 (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))))
% 0.40/0.60  (step t76.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= tptp.b (tptp.multiply tptp.identity tptp.b)))) :rule forall_inst :args ((:= X tptp.b)))
% 0.40/0.60  (step t76.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= tptp.b (tptp.multiply tptp.identity tptp.b))) :rule or :premises (t76.t1))
% 0.40/0.60  (step t76.t3 (cl (= tptp.b (tptp.multiply tptp.identity tptp.b))) :rule resolution :premises (t76.t2 t76.a0))
% 0.40/0.60  (step t76 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= tptp.b (tptp.multiply tptp.identity tptp.b))) :rule subproof :discharge (t76.a0))
% 0.40/0.60  (step t77 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.b (tptp.multiply tptp.identity tptp.b))) (= tptp.b (tptp.multiply tptp.identity tptp.b))) :rule resolution :premises (t75 t76))
% 0.40/0.60  (step t78 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b)))) :rule implies_neg2)
% 0.40/0.60  (step t79 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.b (tptp.multiply tptp.identity tptp.b))) (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.b (tptp.multiply tptp.identity tptp.b)))) :rule resolution :premises (t77 t78))
% 0.40/0.60  (step t80 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.b (tptp.multiply tptp.identity tptp.b)))) :rule contraction :premises (t79))
% 0.40/0.60  (step t81 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= tptp.b (tptp.multiply tptp.identity tptp.b))) :rule implies :premises (t80))
% 0.40/0.60  (step t82 (cl (not (= (forall ((X $$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 $$unsorted)) (= X (tptp.multiply tptp.identity X)))) :rule equiv_pos2)
% 0.40/0.60  (anchor :step t83 :args ((X $$unsorted) (:= X X)))
% 0.40/0.60  (step t83.t1 (cl (= X X)) :rule refl)
% 0.40/0.60  (step t83.t2 (cl (= (= (tptp.multiply tptp.identity X) X) (= X (tptp.multiply tptp.identity X)))) :rule all_simplify)
% 0.40/0.60  (step t83 (cl (= (forall ((X $$unsorted)) (= (tptp.multiply tptp.identity X) X)) (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))))) :rule bind)
% 0.40/0.60  (step t84 (cl (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) :rule resolution :premises (t82 t83 a0))
% 0.40/0.60  (step t85 (cl (= tptp.b (tptp.multiply tptp.identity tptp.b))) :rule resolution :premises (t81 t84))
% 0.40/0.60  (step t86 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) :rule implies_neg1)
% 0.40/0.60  (anchor :step t87)
% 0.40/0.60  (assume t87.a0 (forall ((Y $$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)))))
% 0.40/0.60  (step t87.t1 (cl (or (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))))) :rule forall_inst :args ((:= Y tptp.a) (:= Z (tptp.greatest_lower_bound tptp.a tptp.identity)) (:= X tptp.b)))
% 0.40/0.60  (step t87.t2 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) :rule or :premises (t87.t1))
% 0.40/0.60  (step t87.t3 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) :rule resolution :premises (t87.t2 t87.a0))
% 0.40/0.60  (step t87 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) :rule subproof :discharge (t87.a0))
% 0.40/0.60  (step t88 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) :rule resolution :premises (t86 t87))
% 0.40/0.60  (step t89 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))))) :rule implies_neg2)
% 0.40/0.60  (step t90 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))))) :rule resolution :premises (t88 t89))
% 0.40/0.60  (step t91 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b))))) :rule contraction :premises (t90))
% 0.40/0.60  (step t92 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) :rule implies :premises (t91))
% 0.40/0.60  (step t93 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)) tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.identity) tptp.b)))) :rule resolution :premises (t92 a13))
% 0.40/0.60  (step t94 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) :rule implies_neg1)
% 0.40/0.60  (anchor :step t95)
% 0.40/0.60  (assume t95.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))))
% 0.40/0.60  (step t95.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))))) :rule forall_inst :args ((:= X tptp.b) (:= Y tptp.identity)))
% 0.40/0.60  (step t95.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) :rule or :premises (t95.t1))
% 0.40/0.60  (step t95.t3 (cl (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) :rule resolution :premises (t95.t2 t95.a0))
% 0.40/0.60  (step t95 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) :rule subproof :discharge (t95.a0))
% 0.40/0.60  (step t96 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) :rule resolution :premises (t94 t95))
% 0.40/0.60  (step t97 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) (not (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))))) :rule implies_neg2)
% 0.40/0.60  (step t98 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))))) :rule resolution :premises (t96 t97))
% 0.40/0.60  (step t99 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity))))) :rule contraction :premises (t98))
% 0.40/0.60  (step t100 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) :rule implies :premises (t99))
% 0.40/0.60  (step t101 (cl (not (= (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)) X)) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))))) (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)) X))) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) :rule equiv_pos2)
% 0.40/0.60  (anchor :step t102 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y)))
% 0.40/0.60  (step t102.t1 (cl (= X X)) :rule refl)
% 0.40/0.60  (step t102.t2 (cl (= Y Y)) :rule refl)
% 0.40/0.60  (step t102.t3 (cl (= (= (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)) X) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) :rule all_simplify)
% 0.40/0.60  (step t102 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)) X)) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))))) :rule bind)
% 0.40/0.60  (step t103 (cl (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) :rule resolution :premises (t101 t102 a9))
% 0.40/0.60  (step t104 (cl (= tptp.b (tptp.least_upper_bound tptp.b (tptp.greatest_lower_bound tptp.b tptp.identity)))) :rule resolution :premises (t100 t103))
% 0.40/0.60  (step t105 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) :rule implies_neg1)
% 0.40/0.60  (anchor :step t106)
% 0.40/0.60  (assume t106.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))))
% 0.40/0.60  (step t106.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule forall_inst :args ((:= X tptp.a) (:= Y tptp.identity)))
% 0.40/0.60  (step t106.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule or :premises (t106.t1))
% 0.40/0.60  (step t106.t3 (cl (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule resolution :premises (t106.t2 t106.a0))
% 0.40/0.60  (step t106 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule subproof :discharge (t106.a0))
% 0.40/0.60  (step t107 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule resolution :premises (t105 t106))
% 0.40/0.60  (step t108 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule implies_neg2)
% 0.40/0.60  (step t109 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule resolution :premises (t107 t108))
% 0.40/0.60  (step t110 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) :rule contraction :premises (t109))
% 0.40/0.60  (step t111 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule implies :premises (t110))
% 0.40/0.60  (step t112 (cl (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule resolution :premises (t111 t103))
% 0.40/0.60  (step t113 (cl (=> (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X)))) :rule implies_neg1)
% 0.40/0.60  (anchor :step t114)
% 0.40/0.60  (assume t114.a0 (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X))))
% 0.40/0.60  (step t114.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)))) :rule forall_inst :args ((:= X tptp.b)))
% 0.40/0.60  (step t114.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) :rule or :premises (t114.t1))
% 0.40/0.60  (step t114.t3 (cl (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) :rule resolution :premises (t114.t2 t114.a0))
% 0.40/0.60  (step t114 (cl (not (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) :rule subproof :discharge (t114.a0))
% 0.40/0.60  (step t115 (cl (=> (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) :rule resolution :premises (t113 t114))
% 0.40/0.60  (step t116 (cl (=> (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) (not (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)))) :rule implies_neg2)
% 0.40/0.60  (step t117 (cl (=> (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) (=> (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)))) :rule resolution :premises (t115 t116))
% 0.40/0.60  (step t118 (cl (=> (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b)))) :rule contraction :premises (t117))
% 0.40/0.60  (step t119 (cl (not (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X)))) (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) :rule implies :premises (t118))
% 0.40/0.60  (step t120 (cl (not (= (forall ((X $$unsorted)) (= (tptp.greatest_lower_bound X X) X)) (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X))))) (not (forall ((X $$unsorted)) (= (tptp.greatest_lower_bound X X) X))) (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X)))) :rule equiv_pos2)
% 0.40/0.60  (anchor :step t121 :args ((X $$unsorted) (:= X X)))
% 0.40/0.60  (step t121.t1 (cl (= X X)) :rule refl)
% 0.40/0.60  (step t121.t2 (cl (= (= (tptp.greatest_lower_bound X X) X) (= X (tptp.greatest_lower_bound X X)))) :rule all_simplify)
% 0.40/0.60  (step t121 (cl (= (forall ((X $$unsorted)) (= (tptp.greatest_lower_bound X X) X)) (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X))))) :rule bind)
% 0.40/0.60  (step t122 (cl (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X)))) :rule resolution :premises (t120 t121 a8))
% 0.40/0.60  (step t123 (cl (= tptp.b (tptp.greatest_lower_bound tptp.b tptp.b))) :rule resolution :premises (t119 t122))
% 0.40/0.60  (step t124 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) :rule implies_neg1)
% 0.40/0.60  (anchor :step t125)
% 0.40/0.60  (assume t125.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))))
% 0.40/0.60  (step t125.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) :rule forall_inst :args ((:= X tptp.identity) (:= Y tptp.a)))
% 0.40/0.60  (step t125.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) :rule or :premises (t125.t1))
% 0.40/0.60  (step t125.t3 (cl (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) :rule resolution :premises (t125.t2 t125.a0))
% 0.40/0.60  (step t125 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) :rule subproof :discharge (t125.a0))
% 0.40/0.60  (step t126 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) :rule resolution :premises (t124 t125))
% 0.40/0.60  (step t127 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) :rule implies_neg2)
% 0.40/0.60  (step t128 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) :rule resolution :premises (t126 t127))
% 0.40/0.60  (step t129 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))))) :rule contraction :premises (t128))
% 0.40/0.60  (step t130 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) :rule implies :premises (t129))
% 0.40/0.60  (step t131 (cl (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a)))) :rule resolution :premises (t130 t103))
% 0.40/0.60  (step t132 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) :rule implies_neg1)
% 0.40/0.60  (anchor :step t133)
% 0.40/0.60  (assume t133.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))))
% 0.40/0.60  (step t133.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)))) :rule forall_inst :args ((:= X tptp.identity) (:= Y (tptp.multiply tptp.a tptp.b))))
% 0.40/0.60  (step t133.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) :rule or :premises (t133.t1))
% 0.40/0.60  (step t133.t3 (cl (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) :rule resolution :premises (t133.t2 t133.a0))
% 0.40/0.60  (step t133 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) :rule subproof :discharge (t133.a0))
% 0.40/0.60  (step t134 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) :rule resolution :premises (t132 t133))
% 0.40/0.60  (step t135 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (not (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)))) :rule implies_neg2)
% 0.40/0.60  (step t136 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)))) :rule resolution :premises (t134 t135))
% 0.40/0.60  (step t137 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)))) :rule contraction :premises (t136))
% 0.40/0.60  (step t138 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) :rule implies :premises (t137))
% 0.40/0.60  (step t139 (cl (= (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) :rule resolution :premises (t138 a4))
% 0.40/0.60  (step t140 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) :rule implies_neg1)
% 0.40/0.60  (anchor :step t141)
% 0.40/0.60  (assume t141.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))))
% 0.40/0.60  (step t141.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)))) :rule forall_inst :args ((:= X tptp.identity) (:= Y tptp.b)))
% 0.40/0.60  (step t141.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) :rule or :premises (t141.t1))
% 0.40/0.60  (step t141.t3 (cl (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) :rule resolution :premises (t141.t2 t141.a0))
% 0.40/0.60  (step t141 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) :rule subproof :discharge (t141.a0))
% 0.40/0.60  (step t142 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) :rule resolution :premises (t140 t141))
% 0.40/0.60  (step t143 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)))) :rule implies_neg2)
% 0.40/0.60  (step t144 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)))) :rule resolution :premises (t142 t143))
% 0.40/0.60  (step t145 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity)))) :rule contraction :premises (t144))
% 0.40/0.60  (step t146 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) :rule implies :premises (t145))
% 0.40/0.60  (step t147 (cl (= (tptp.greatest_lower_bound tptp.identity tptp.b) (tptp.greatest_lower_bound tptp.b tptp.identity))) :rule resolution :premises (t146 a3))
% 0.40/0.60  (step t148 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) :rule implies_neg1)
% 0.40/0.60  (anchor :step t149)
% 0.40/0.60  (assume t149.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))))
% 0.40/0.60  (step t149.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule forall_inst :args ((:= X tptp.identity) (:= Y tptp.a)))
% 0.40/0.60  (step t149.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) :rule or :premises (t149.t1))
% 0.40/0.60  (step t149.t3 (cl (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) :rule resolution :premises (t149.t2 t149.a0))
% 0.40/0.60  (step t149 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) :rule subproof :discharge (t149.a0))
% 0.40/0.60  (step t150 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) :rule resolution :premises (t148 t149))
% 0.40/0.60  (step t151 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule implies_neg2)
% 0.40/0.60  (step t152 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule resolution :premises (t150 t151))
% 0.40/0.60  (step t153 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity)))) :rule contraction :premises (t152))
% 0.40/0.60  (step t154 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) :rule implies :premises (t153))
% 0.40/0.60  (step t155 (cl (= (tptp.greatest_lower_bound tptp.identity tptp.a) (tptp.greatest_lower_bound tptp.a tptp.identity))) :rule resolution :premises (t154 a3))
% 0.40/0.60  (step t156 (cl (not (= (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound tptp.identity (tptp.multiply tptp.a tptp.b))))) :rule not_symm :premises (a17))
% 0.40/0.60  (step t157 (cl (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.b))) :rule symm :premises (a16))
% 0.40/0.60  (step t158 (cl (= tptp.identity (tptp.greatest_lower_bound tptp.identity tptp.a))) :rule symm :premises (a15))
% 0.40/0.60  (step t159 (cl) :rule resolution :premises (t66 t74 t85 t93 t104 t112 t123 t131 t139 t147 t155 t156 t157 t158))
% 0.40/0.60  
% 0.40/0.60  % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.yHWSQS77WP/cvc5---1.0.5_27924.smt2
% 0.40/0.60  % cvc5---1.0.5 exiting
% 0.40/0.60  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------