%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : GRP186-4 : TPTP v8.2.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : do_cvc5 %s %d

% Computer : n025.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 16:53:43 EDT 2024

% Result   : Unsatisfiable 0.21s 0.56s
% Output   : Proof 0.41s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : GRP186-4 : TPTP v8.2.0. Bugfixed v1.2.1.
% 0.12/0.15  % Command    : do_cvc5 %s %d
% 0.14/0.36  % Computer : n025.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Sun May 26 17:57:54 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.21/0.52  %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.52  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.56  % SZS status Unsatisfiable for /export/starexec/sandbox2/tmp/tmp.cT6ZEvi7oV/cvc5---1.0.5_28815.smt2
% 0.21/0.56  % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.cT6ZEvi7oV/cvc5---1.0.5_28815.smt2
% 0.21/0.57  (assume a0 (forall ((X $$unsorted)) (= (tptp.multiply tptp.identity X) X)))
% 0.21/0.57  (assume a1 (forall ((X $$unsorted)) (= (tptp.multiply (tptp.inverse X) X) tptp.identity)))
% 0.21/0.57  (assume a2 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 0.21/0.57  (assume a3 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))))
% 0.21/0.57  (assume a4 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))))
% 0.21/0.57  (assume a5 (forall ((X $$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))))
% 0.21/0.57  (assume a6 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))))
% 0.21/0.57  (assume a7 (forall ((X $$unsorted)) (= (tptp.least_upper_bound X X) X)))
% 0.21/0.57  (assume a8 (forall ((X $$unsorted)) (= (tptp.greatest_lower_bound X X) X)))
% 0.21/0.57  (assume a9 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)) X)))
% 0.21/0.57  (assume a10 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)) X)))
% 0.21/0.57  (assume a11 (forall ((X $$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)))))
% 0.21/0.57  (assume a12 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))))
% 0.21/0.57  (assume a13 (forall ((Y $$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)))))
% 0.21/0.57  (assume a14 (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))))
% 0.21/0.57  (assume a15 (= (tptp.inverse tptp.identity) tptp.identity))
% 0.21/0.57  (assume a16 (forall ((X $$unsorted)) (= (tptp.inverse (tptp.inverse X)) X)))
% 0.21/0.57  (assume a17 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))))
% 0.21/0.57  (assume a18 (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity) (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)))))
% 0.21/0.57  (step t1 (cl (and (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))) :rule and_neg)
% 0.21/0.57  (step t2 (cl (=> (and (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity) (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)))) (and (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))) :rule implies_neg1)
% 0.21/0.57  (anchor :step t3)
% 0.21/0.57  (assume t3.a0 (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))))
% 0.21/0.57  (assume t3.a1 (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))))
% 0.21/0.57  (assume t3.a2 (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))
% 0.21/0.57  (assume t3.a3 (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))
% 0.21/0.57  (assume t3.a4 (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))
% 0.21/0.57  (step t3.t1 (cl (=> (and (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity) (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)))) (and (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule implies_neg1)
% 0.21/0.57  (anchor :step t3.t2)
% 0.21/0.57  (assume t3.t2.a0 (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))))
% 0.21/0.57  (assume t3.t2.a1 (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))
% 0.21/0.57  (assume t3.t2.a2 (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))))
% 0.21/0.57  (assume t3.t2.a3 (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))
% 0.21/0.57  (assume t3.t2.a4 (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))
% 0.21/0.57  (step t3.t2.t1 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.identity)) :rule symm :premises (t3.t2.a4))
% 0.21/0.57  (step t3.t2.t2 (cl (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule symm :premises (t3.t2.t1))
% 0.21/0.57  (step t3.t2.t3 (cl (= (tptp.inverse (tptp.inverse tptp.a)) tptp.a)) :rule symm :premises (t3.t2.a3))
% 0.21/0.57  (step t3.t2.t4 (cl (= (tptp.inverse tptp.a) (tptp.inverse tptp.a))) :rule refl)
% 0.21/0.57  (step t3.t2.t5 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) :rule cong :premises (t3.t2.t3 t3.t2.t4))
% 0.21/0.57  (step t3.t2.t6 (cl (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a)))) :rule trans :premises (t3.t2.t2 t3.t2.t5))
% 0.21/0.57  (step t3.t2.t7 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule cong :premises (t3.t2.a2 t3.t2.t6))
% 0.21/0.57  (step t3.t2.t8 (cl (= (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (tptp.multiply tptp.a tptp.b))) :rule symm :premises (t3.t2.a2))
% 0.21/0.57  (step t3.t2.t9 (cl (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) :rule refl)
% 0.21/0.57  (step t3.t2.t10 (cl (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule cong :premises (t3.t2.t8 t3.t2.t9))
% 0.21/0.57  (step t3.t2.t11 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)))) :rule symm :premises (t3.t2.a1))
% 0.21/0.57  (step t3.t2.t12 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)))) :rule symm :premises (t3.t2.a0))
% 0.21/0.57  (step t3.t2.t13 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity) (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)))) :rule trans :premises (t3.t2.t7 t3.t2.t10 t3.t2.t11 t3.t2.t12))
% 0.21/0.57  (step t3.t2 (cl (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity) (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)))) :rule subproof :discharge (t3.t2.a0 t3.t2.a1 t3.t2.a2 t3.t2.a3 t3.t2.a4))
% 0.21/0.57  (step t3.t3 (cl (not (and (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)))) :rule and_pos)
% 0.21/0.57  (step t3.t4 (cl (not (and (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule and_pos)
% 0.21/0.57  (step t3.t5 (cl (not (and (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)))) :rule and_pos)
% 0.21/0.57  (step t3.t6 (cl (not (and (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule and_pos)
% 0.21/0.57  (step t3.t7 (cl (not (and (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule and_pos)
% 0.21/0.57  (step t3.t8 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity) (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b))) (not (and (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (and (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (and (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (and (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (and (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) :rule resolution :premises (t3.t2 t3.t3 t3.t4 t3.t5 t3.t6 t3.t7))
% 0.21/0.57  (step t3.t9 (cl (not (and (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (and (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (and (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (and (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (and (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity) (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)))) :rule reordering :premises (t3.t8))
% 0.21/0.57  (step t3.t10 (cl (not (and (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity) (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)))) :rule contraction :premises (t3.t9))
% 0.21/0.57  (step t3.t11 (cl (=> (and (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity) (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity) (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)))) :rule resolution :premises (t3.t1 t3.t10))
% 0.21/0.57  (step t3.t12 (cl (=> (and (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity) (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity) (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b))))) :rule implies_neg2)
% 0.21/0.57  (step t3.t13 (cl (=> (and (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity) (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)))) (=> (and (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity) (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b))))) :rule resolution :premises (t3.t11 t3.t12))
% 0.21/0.57  (step t3.t14 (cl (=> (and (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity) (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b))))) :rule contraction :premises (t3.t13))
% 0.21/0.57  (step t3.t15 (cl (not (and (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity) (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)))) :rule implies :premises (t3.t14))
% 0.21/0.57  (step t3.t16 (cl (and (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule and_neg)
% 0.21/0.57  (step t3.t17 (cl (and (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule resolution :premises (t3.t16 t3.a1 t3.a2 t3.a0 t3.a4 t3.a3))
% 0.21/0.57  (step t3.t18 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity) (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)))) :rule resolution :premises (t3.t15 t3.t17))
% 0.21/0.57  (step t3 (cl (not (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity) (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)))) :rule subproof :discharge (t3.a0 t3.a1 t3.a2 t3.a3 t3.a4))
% 0.21/0.57  (step t4 (cl (not (and (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)))) :rule and_pos)
% 0.21/0.57  (step t5 (cl (not (and (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)))) :rule and_pos)
% 0.21/0.57  (step t6 (cl (not (and (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule and_pos)
% 0.21/0.57  (step t7 (cl (not (and (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule and_pos)
% 0.21/0.57  (step t8 (cl (not (and (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule and_pos)
% 0.21/0.57  (step t9 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity) (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b))) (not (and (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))) (not (and (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))) (not (and (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))) (not (and (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))) (not (and (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))))) :rule resolution :premises (t3 t4 t5 t6 t7 t8))
% 0.21/0.57  (step t10 (cl (not (and (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))) (not (and (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))) (not (and (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))) (not (and (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))) (not (and (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity) (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)))) :rule reordering :premises (t9))
% 0.21/0.57  (step t11 (cl (not (and (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity) (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)))) :rule contraction :premises (t10))
% 0.21/0.57  (step t12 (cl (=> (and (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity) (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity) (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)))) :rule resolution :premises (t2 t11))
% 0.21/0.57  (step t13 (cl (=> (and (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity) (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity) (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b))))) :rule implies_neg2)
% 0.21/0.57  (step t14 (cl (=> (and (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity) (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)))) (=> (and (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity) (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b))))) :rule resolution :premises (t12 t13))
% 0.21/0.57  (step t15 (cl (=> (and (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity) (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b))))) :rule contraction :premises (t14))
% 0.21/0.57  (step t16 (cl (not (and (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity) (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)))) :rule implies :premises (t15))
% 0.21/0.57  (step t17 (cl (not (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity) (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)))) :rule resolution :premises (t1 t16))
% 0.21/0.57  (step t18 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity) (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b))) (not (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))) :rule reordering :premises (t17))
% 0.21/0.57  (step t19 (cl (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) :rule implies_neg1)
% 0.21/0.57  (anchor :step t20)
% 0.21/0.57  (assume t20.a0 (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))))
% 0.21/0.57  (step t20.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))) :rule forall_inst :args ((:= X tptp.a)))
% 0.21/0.57  (step t20.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule or :premises (t20.t1))
% 0.21/0.57  (step t20.t3 (cl (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule resolution :premises (t20.t2 t20.a0))
% 0.21/0.57  (step t20 (cl (not (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule subproof :discharge (t20.a0))
% 0.21/0.57  (step t21 (cl (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule resolution :premises (t19 t20))
% 0.21/0.57  (step t22 (cl (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))) :rule implies_neg2)
% 0.21/0.57  (step t23 (cl (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))) :rule resolution :premises (t21 t22))
% 0.21/0.57  (step t24 (cl (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))) :rule contraction :premises (t23))
% 0.21/0.57  (step t25 (cl (not (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule implies :premises (t24))
% 0.21/0.57  (step t26 (cl (not (= (forall ((X $$unsorted)) (= (tptp.inverse (tptp.inverse X)) X)) (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))))) (not (forall ((X $$unsorted)) (= (tptp.inverse (tptp.inverse X)) X))) (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) :rule equiv_pos2)
% 0.21/0.57  (anchor :step t27 :args ((X $$unsorted) (:= X X)))
% 0.21/0.57  (step t27.t1 (cl (= X X)) :rule refl)
% 0.21/0.57  (step t27.t2 (cl (= (= (tptp.inverse (tptp.inverse X)) X) (= X (tptp.inverse (tptp.inverse X))))) :rule all_simplify)
% 0.21/0.57  (step t27 (cl (= (forall ((X $$unsorted)) (= (tptp.inverse (tptp.inverse X)) X)) (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))))) :rule bind)
% 0.21/0.57  (step t28 (cl (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) :rule resolution :premises (t26 t27 a16))
% 0.21/0.57  (step t29 (cl (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule resolution :premises (t25 t28))
% 0.21/0.57  (step t30 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) :rule implies_neg1)
% 0.21/0.57  (anchor :step t31)
% 0.21/0.57  (assume t31.a0 (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))))
% 0.21/0.57  (step t31.t1 (cl (or (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.a))))
% 0.21/0.57  (step t31.t2 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule or :premises (t31.t1))
% 0.21/0.57  (step t31.t3 (cl (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule resolution :premises (t31.t2 t31.a0))
% 0.21/0.57  (step t31 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule subproof :discharge (t31.a0))
% 0.21/0.57  (step t32 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule resolution :premises (t30 t31))
% 0.21/0.57  (step t33 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule implies_neg2)
% 0.21/0.57  (step t34 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule resolution :premises (t32 t33))
% 0.21/0.57  (step t35 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule contraction :premises (t34))
% 0.21/0.57  (step t36 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule implies :premises (t35))
% 0.21/0.57  (step t37 (cl (not (= (forall ((X $$unsorted)) (= (tptp.multiply (tptp.inverse X) X) tptp.identity)) (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))))) (not (forall ((X $$unsorted)) (= (tptp.multiply (tptp.inverse X) X) tptp.identity))) (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) :rule equiv_pos2)
% 0.21/0.57  (anchor :step t38 :args ((X $$unsorted) (:= X X)))
% 0.21/0.57  (step t38.t1 (cl (= X X)) :rule refl)
% 0.21/0.57  (step t38.t2 (cl (= (= (tptp.multiply (tptp.inverse X) X) tptp.identity) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) :rule all_simplify)
% 0.21/0.57  (step t38 (cl (= (forall ((X $$unsorted)) (= (tptp.multiply (tptp.inverse X) X) tptp.identity)) (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))))) :rule bind)
% 0.21/0.57  (step t39 (cl (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) :rule resolution :premises (t37 t38 a1))
% 0.21/0.57  (step t40 (cl (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule resolution :premises (t36 t39))
% 0.21/0.57  (step t41 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) :rule implies_neg1)
% 0.21/0.57  (anchor :step t42)
% 0.21/0.57  (assume t42.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))))
% 0.21/0.57  (step t42.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) :rule forall_inst :args ((:= X (tptp.multiply tptp.a (tptp.inverse tptp.a))) (:= Y (tptp.multiply tptp.a tptp.b))))
% 0.21/0.57  (step t42.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule or :premises (t42.t1))
% 0.21/0.57  (step t42.t3 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule resolution :premises (t42.t2 t42.a0))
% 0.21/0.57  (step t42 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule subproof :discharge (t42.a0))
% 0.21/0.57  (step t43 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule resolution :premises (t41 t42))
% 0.21/0.57  (step t44 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) :rule implies_neg2)
% 0.21/0.57  (step t45 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) :rule resolution :premises (t43 t44))
% 0.21/0.57  (step t46 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) :rule contraction :premises (t45))
% 0.21/0.57  (step t47 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule implies :premises (t46))
% 0.21/0.57  (step t48 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule resolution :premises (t47 a4))
% 0.21/0.57  (step t49 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z))))) :rule implies_neg1)
% 0.21/0.57  (anchor :step t50)
% 0.21/0.57  (assume t50.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))))
% 0.21/0.57  (step t50.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))))) :rule forall_inst :args ((:= X tptp.a) (:= Y (tptp.inverse tptp.a)) (:= Z tptp.b)))
% 0.21/0.57  (step t50.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)))) :rule or :premises (t50.t1))
% 0.21/0.57  (step t50.t3 (cl (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)))) :rule resolution :premises (t50.t2 t50.a0))
% 0.21/0.57  (step t50 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)))) :rule subproof :discharge (t50.a0))
% 0.21/0.57  (step t51 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)))) :rule resolution :premises (t49 t50))
% 0.21/0.57  (step t52 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))))) :rule implies_neg2)
% 0.21/0.57  (step t53 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))))) :rule resolution :premises (t51 t52))
% 0.21/0.57  (step t54 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b))))) :rule contraction :premises (t53))
% 0.21/0.57  (step t55 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)))) :rule implies :premises (t54))
% 0.21/0.57  (step t56 (cl (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.b)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.b)))) :rule resolution :premises (t55 a11))
% 0.21/0.57  (step t57 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)))) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) :rule implies_neg1)
% 0.21/0.57  (anchor :step t58)
% 0.21/0.57  (assume t58.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))))
% 0.21/0.57  (step t58.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))))) :rule forall_inst :args ((:= X (tptp.multiply tptp.a tptp.b)) (:= Y tptp.identity)))
% 0.21/0.57  (step t58.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)))) :rule or :premises (t58.t1))
% 0.21/0.57  (step t58.t3 (cl (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)))) :rule resolution :premises (t58.t2 t58.a0))
% 0.21/0.57  (step t58 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)))) :rule subproof :discharge (t58.a0))
% 0.21/0.57  (step t59 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)))) (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)))) :rule resolution :premises (t57 t58))
% 0.21/0.57  (step t60 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)))) (not (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))))) :rule implies_neg2)
% 0.21/0.57  (step t61 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))))) :rule resolution :premises (t59 t60))
% 0.21/0.57  (step t62 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity))))) :rule contraction :premises (t61))
% 0.21/0.57  (step t63 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)))) :rule implies :premises (t62))
% 0.21/0.57  (step t64 (cl (not (= (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)) X)) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))))) (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)) X))) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) :rule equiv_pos2)
% 0.21/0.57  (anchor :step t65 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y)))
% 0.21/0.57  (step t65.t1 (cl (= X X)) :rule refl)
% 0.21/0.57  (step t65.t2 (cl (= Y Y)) :rule refl)
% 0.21/0.57  (step t65.t3 (cl (= (= (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)) X) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) :rule all_simplify)
% 0.21/0.57  (step t65 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)) X)) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))))) :rule bind)
% 0.21/0.57  (step t66 (cl (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) :rule resolution :premises (t64 t65 a10))
% 0.21/0.57  (step t67 (cl (= (tptp.multiply tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.b) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.b) tptp.identity)))) :rule resolution :premises (t63 t66))
% 0.21/0.57  (step t68 (cl) :rule resolution :premises (t18 t29 t40 t48 t56 t67 a18))
% 0.21/0.57  
% 0.41/0.58  % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.cT6ZEvi7oV/cvc5---1.0.5_28815.smt2
% 0.41/0.58  % cvc5---1.0.5 exiting
% 0.41/0.58  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------